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Aim # 14: How Do We Determine the Income from our Investments? CD Rate is 1.2%

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Do Now Julie Fee is a real estate broker who earns 8.5% commission on each house she sells. If she earned $35,700 on a house she sold, what was the selling price of the house? Answer: $420,000

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Minilesson: Formula for Interest Earned on a Deposit: This is I = prt Where I = simple interest earned p = your original deposit r = interest rate as a decimal t = period of time (in our case, 1 yr)

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Minilesson (cont’d): For any question, Either follow the wording of the verbal problem, OR Set-up a table (to help organize your thoughts) YOU decide

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Minilesson (cont’d): Either follow the wording of the verbal problem, Interest Rate for Investment X Amount Invested = Amount Earned

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Minilesson (cont’d): Either follow the wording of the verbal problem, Amt Earned Investment # 1 + = Total Amount Earned from BOTH Investments Amt Earned Investment # 2

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Minilesson (cont’d): Set-up a table (to help organize your thoughts) Interest Rate X Amt Earned = Amt Invested

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Minilesson (cont’d): Set-up a table (to help organize your thoughts) Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2

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Guided Practice Handout, qq. 318 – 319, qq. 1, 2, 7

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Independent Practice Handout Aim # 14, qq. 5, 6, 8, 9, 10

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Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.035m 0.035m 0.089000 —m0.08(9000 —m) Note: First investment income exceeds 2 nd by $ 16.

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Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.035m 0.035m 0.089000 —m0.08(9000 —m) Note: 1 st minus 2 nd equals 16

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Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.035m 0.035m 0.089000 —m0.08(9000 —m)

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Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.035m 0.035m 0.089000 —m0.08(9000 —m) Multiply through by 1000.

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Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.035m 0.035m 0.089000 —m0.08(9000 —m) Distribute 80 across parentheses.

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Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.035m 0.035m 0.089000 —m0.08(9000 —m) NOTICE: Minus sign changed to plus.

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Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8% Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.035m 0.035m 0.089000 —m0.08(9000 —m) Combine like terms.

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Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.035m 0.035m 0.089000 —m0.08(9000 —m)

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Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.035m 0.035m 0.089000 —m0.08(9000 —m) Divide both sides by coefficient 115.

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Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % ANSWER $6,400 invested at 3.5% $2,600 invested at 8%

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Independent Practice (cont’d) Question 5 Let m = amt invested at 3.5 % 9000 — m = amt invested at 8 % CHECK $6,400 invested at 3.5% $2,600 invested at 8% 0.035(6400) = 2240.08(2600) = 208 224 − 208 = 16 It works!!

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Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 9000 — (m+2m) = amt invested at 2 % The remaining is $9000 minus the sum of the first two investments

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Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 9000 — 3m = amt invested at 2 % The remaining is $9000 minus the sum of the first two investments

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Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.06m 0.06m 0.02 9000 —3m 0.02(9000 —3m) Note: The money earned on the three investments is $360. 9000 — 3m = amt invested at 2 % The remaining is $9000 minus the sum of the first two investments Investment # 3 0.045 2m 0.045(2m)

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Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.06m 0.06m 0.02 9000 —3m 0.02(9000 —3m) 9000 — 3m = amt invested at 2 % Investment # 3 0.045 2m 0.045(2m) Note: 1 st plus 2 nd plus 3 rd equals 360

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Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.06m 0.06m 0.02 9000 —3m 0.02(9000 —3m) 9000 — 3m = amt invested at 2 % Investment # 3 0.045 2m 0.045(2m)

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Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.06m 0.06m 0.02 9000 —3m 0.02(9000 —3m) 9000 — 3m = amt invested at 2 % Investment # 3 0.045 2m 0.045(2m)

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Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.06m 0.06m 0.02 9000 —3m 0.02(9000 —3m) 9000 — 3m = amt invested at 2 % Investment # 3 0.045 2m 0.045(2m)

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Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.06m 0.06m 0.02 9000 —3m 0.02(9000 —3m) 9000 — 3m = amt invested at 2 % Investment # 3 0.045 2m 0.045(2m) Combine like terms.

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Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.06m 0.06m 0.02 9000 —3m 0.02(9000 —3m) 9000 — 3m = amt invested at 2 % Investment # 3 0.045 2m 0.045(2m) Combine like terms. The 60m cancels out.

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Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.06m 0.06m 0.02 9000 —3m 0.02(9000 —3m) 9000 — 3m = amt invested at 2 % Investment # 3 0.045 2m 0.045(2m) Subtract from both sides.

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Independent Practice (cont’d) Question 6 Let m = amt invested at 6 % 2m = amt invested at 4.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.06m 0.06m 0.02 9000 —3m 0.02(9000 —3m) 9000 — 3m = amt invested at 2 % Investment # 3 0.045 2m 0.045(2m) Divide both sides.

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Independent Practice (cont’d) Question 6 ANSWER $2,000 invested at 6% $4,000 invested at 4.5% $3,000 invested at 2% Let m = amt invested at 6 % 2m = amt invested at 4.5 % 9000 — 3m = amt invested at 2 %

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Independent Practice (cont’d) Question 6 CHECK! 0.06(2,000) + 0.045(4000) + 0.02(3000) 120 + 180 + 60 Let m = amt invested at 6 % 2m = amt invested at 4.5 % 9000 — 3m = amt invested at 2 % 360

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Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.03m 0.03m 0.058000 —m0.05(8000 —m) Note: Man LOST money from 2 nd Investment.

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Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.03m 0.03m 0.058000 —m0.05(8000 —m) Note: GAIN of 1 st + LOSS 2 nd = Net Income.

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Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.03m 0.03m 0.058000 —m—0.05(8000 —m) Note: GAIN of 1 st + LOSS 2 nd = Net Income.

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Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.03m 0.03m 0.058000 —m—0.05(8000 —m)

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Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.03m 0.03m 0.058000 —m—0.05(8000 —m)

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Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.03m 0.03m 0.058000 —m—0.05(8000 —m) Distributive Property changes signs.

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Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.03m 0.03m 0.058000 —m—0.05(8000 —m)

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Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.03m 0.03m 0.058000 —m—0.05(8000 —m)

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Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.03m 0.03m 0.058000 —m—0.05(8000 —m)

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Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % ANSWER $6,000 invested at 3% $2,000 invested at 5%

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Independent Practice (cont’d) Question 8 Let m = amt invested at 3 % 8000 — m = amt invested at 5 % CHECK 0.03(6,000) = $180 MINUS 0.05(2,000) = $100 Net Gain = $ 80

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Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.05m 0.05m 0.0359600 —m 0.035(9600 —m) Note: 1 st Investment yields twice 2 nd Investment.

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Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.05m 0.05m 0.0359600 —m 0.035(9600 —m) Twice the amt earned from 2 nd investment

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Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.05m 0.05m 0.0359600 —m 0.035(9600 —m) Doubled 0.035 Doubled 0.35

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Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.05m 0.05m 0.0359600 —m 0.035(9600 —m) Multiply through by 100

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Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.05m 0.05m 0.0359600 —m 0.035(9600 —m) Distribute the 7.

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Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.05m 0.05m 0.0359600 —m 0.035(9600 —m)

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Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.05m 0.05m 0.0359600 —m 0.035(9600 —m)

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Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % Interest Rate X Amt Earned = Amt Invested Investment # 1 Investment # 2 0.05m 0.05m 0.0359600 —m 0.035(9600 —m)

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Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % ANSWER $5,600 invested at 5% $4,000 invested at 3.5%

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Independent Practice (cont’d) Question 9 Let m = amt invested at 5 % 9600 — m = amt invested at 3.5 % CHECK 0.05(5600) = 280 0.035(4000) = 140 It works! $280 is twice $140. Yay!

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Independent Practice (cont’d) Question 10 Let E = amt in entire estate Plan: ¼ of the estate is invested at 5%. This means there is now ¾ remaining. 1/3 of ¾ is 1/4, which is then invested at 2%. ¼ plus ¼ is 1/2, so the rest of the estate is ½ (which is invested at 6%.

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Independent Practice (cont’d) Question 10 More Explanation ¼ of the estate is invested at 5%. This means there is now ¾ remaining.

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Independent Practice (cont’d) Question 10 Plan: 1/3 of ¾ is 1/4, which is then invested at 2%. ¼ plus ¼ is 1/2, so the rest of the estate is ½ (which is invested at 6%.

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Independent Practice (cont’d) Question 10 Plan: 1/3 of ¾ is 1/4, which is then invested at 2%. ¼ plus ¼ is 1/2, so the rest of the estate is ½ (which is invested at 6%.

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Independent Practice (cont’d) Question 10 Plan: 1/3 of ¾ is 1/4, which is then invested at 2%. ¼ plus ¼ is 1/2, so the rest of the estate is ½ (which is invested at 6%.

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Independent Practice (cont’d) Question 10 Plan:

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Independent Practice (cont’d) Question 10 Therefore:

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Independent Practice (cont’d) Question 10 Therefore: Fractions were converted into decimals.

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Independent Practice (cont’d) Question 10 Therefore: Multiplied through by 100.

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Independent Practice (cont’d) Question 10 Therefore: Simplified products.

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Independent Practice (cont’d) Question 10 Therefore: Combined like terms.

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Independent Practice (cont’d) Question 10 Therefore: Divided both sides by 4.75

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Independent Practice (cont’d) Question 10 ANSWER The original estate was $16,000.

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Independent Practice (cont’d) Question 10 CHECK The estate was $16,000. 16000/4 = 4000 16000/2 = 8000 TOTAL = 16000 Works here, too!

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Our Textbook, p. 319, qq. 12 –16, EVEN only

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Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 4.8 Solving Equations Containing Fractions.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 4.8 Solving Equations Containing Fractions.

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