1. Investment (Interest) and Mixture Problems

2. Interest Problems page 198 Simple Interest is interest earned on the principle or original amount. Compound interest is interest earned on the principal and on the interest. Simple Interest I=PRT Interest = principal * rate * time rate=interest rate as a decimal 5%=0.05 time = number of years

3. Simple Interest problems A table can be used to make it easier to understand the problem. page 199 Yujung invested $3000, part at 8% and part at 7.5% The total return (interest earned) for one year was $231. How much was invested at each rate. PRT=IPrincipalRateTimeInterest Amount invested at 8% 3000-x0.0811(0.08)(3000-x) Amount invested at 7.5% x0.07511(0.075)(x)

4. 0.08(3000-x) + 0.075x = 231 The interest from each part of the investment adds up to the total interest. if you multiply each term by 1000 to eliminate the decimals, you get: 240,000 – 80x + 75x = 231,000 5x = 9000, x = 1800 Amount invested at 8%3000-x3000-1800 = $1200 Amount invested at 7.5%x$1800

5. Practice Page 200 # 1,2

6. Page 200 #1 PrincipalRateTimeInterest = PRT Amount Invested at 12%x0.1210.12x Amount Invested at 10%18750-x0.1010.10(18750-x) 0.12x +0.10(18750-x)=2117 0.12x+1875-0.10x=2117 0.02x+1875=2117 0.02x=242 x=12100 18750-x=6650 Amount invested at 12% = $12100 amount invested at 10% = $6650

7. Page 200 #2 0.12x + 0.08x + 240 = 760 0.2x = 520 2x =5200 X = 2600 2600 at 12% and 5600 at 8% PrincipalRateTimeInterest = PRT Amount Invested at 12%x0.1210.12x Amount Invested at 8%x + 30000.0810.08(x+3000)

8. Mixture problems page 201 How many liters of a 50% alcohol solution must be added with 80 liters of a 20% alcohol solution to make a 40% alcohol solution? 1.What do we know 2.what do we need to know 3.write equation 4.solve

9. % solution Solution % as decimal amount of substance Amount of the total mixture 50%0.50x0.5x 20%0.20800.2(80) 40%0.40Total x+800.40(x+80) Part Total 0.5x + 0.2(80) = 0.40(x+80) 0.5x +16 = 0.4x + 32 0.1x = 16 x=160 We need 160 liters of 50% solution to mix with the 80 liters of 20% solution which will make a 240 liters 40% solution.

10. Practice Page 202 # 1 (at top of page) typecostAmount (# of lbs)total 32 cents0.32x0.32x 25 cents0.2535-x0.25(35-x) 30 cents0.30350.30(35) 0.32x + 8.75 -0.25x=10.5 0.07x = 1.75 7x = 175 x=25 We need 25 pounds of 32 cent candy and 10 pounds of 25 cent candy

11. 나우웍 /Homework /Dormwork/ 열람실웍 page 203-206 # 1-12