1. Word Problems Involving Investments

2. Investment type problems are a type of mixture problem
Investment type problems are a type of mixture problem. In this type of problem we are mixing money into different accounts. For example…...
Ron Burgandy has $15,000 to invest. He plans to diversify his money by investing it in two different accounts. One account gives 11.5% interest and the other 9% interest. If he wants to make $ in interest in the first year, how much should he place in each account?
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3. The interest of the 2 accounts added together equal the total.
Ron Burgandy has $15,000 to invest. He plans to diversify his money by investing it in two different accounts. One account gives 11.5% interest and the other 9% interest. If he wants to make $ in interest in the first year, how much should he place in each account?
.115
.115x x
.09 x
.09(15000-x)
15,000
The interest of the 2 accounts added together equal the total.
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4. Ron invested $8500 in the 11.5% acct. and $6500 in the 9% acct.
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5. Work them out on paper then check.
Mixture Problems
Work them out on paper then check.
1. Mr. Planter wants to mix 20 lb of macadamia nuts that cost $8.10 per pound with pecans that cost $5.40 per pound. How many pounds of pecans should he use if the mixture is to cost $6.48 per pound?
2. Mr. Planter also wants a 40 lb mixture of pecans and walnuts that will sell for $4.80 per pound. If the pecans cost $5.40 per pound and the walnuts cost $4.40 per pound, how many of each should he use?
3. Eddie invested $2400 in two simple interest accounts. The annual rate in one account is 8% and the annual rate in the other is 11%. How much did he invest in each account if the annual interest totaled $240?
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6. 4. Fred and Irma invested $12,500 in two simple interest accounts
4. Fred and Irma invested $12,500 in two simple interest accounts. One account earns annual simple interest of 7% while the other earns 6%. How much was invested at each rate if each account earned the same interest? Round your answer to the nearest dollar.
5. Bubba has two part time jobs. One pays $7.50 per hour and the other pays $9.00 per hour. Last week he earned $427 while working 50 hours. How many hours did he work at each job?
6. Kim had to pay $1200 in labor for some repairs to the house. The carpenter charged $18 an hour and the painter charged $15 per hour. If she paid for 73 hours of work, how much work was done by each?
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7. 2. 16 pounds of pecans and 24 pounds of walnuts
Mixture Solutions
pounds of pecans
pounds of pecans and 24 pounds of walnuts
3. $800 invested at 8%. and $1600 invested at 11%.
4. $5769 is invested at 7% and $6731 invested at 6%.
5. 15/3 hours at Job 1 and 34 2/3 hours at Job 2
hours by the carpenter and 38 hours of work by the painter.
For complete details click to next slide.
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8. 1. Mr. Planter wants to mix 20 lb of macadamia nuts that cost $8
1. Mr. Planter wants to mix 20 lb of macadamia nuts that cost $8.10 per pound with pecans that cost $5.40 per pound. How many pounds of pecans should he use if the mixture is to cost $6.48 per pound?
lbs
cost
total
macd 20
8.10
162
pecans x
5.40
5.4x
X + 20
6.48
6.48(x+20)
  x = 6.48(x + 20)
x = 6.48x
162 = 6.48x – 5.4x
162 – = 1.08x
32.4 = 1.08x
30 = x
50 = x + 20
30 pounds of pecans will need to be added to the 20 pounds of macadamia nuts to make a mix worth $6.48
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9.    2.   Mr. Planter also wants a 40 lb mixture of pecans and walnuts that will sell for $4.80 per pound. If the pecans cost $5.40 per pound and the walnuts cost $4.40 per pound, how many of each should he use?
lbs
cost
total
Pecans x
5.40
5.4x
walnuts
40 - x
4.40
4.4(40-x) 40
4.80
4.8(40)
5.4x + 4.4(40 – x) + = 40(4.8)
5.4x +176 – 4.4x + = 192
x = 192
x = 16
40 – x = 24
Mr. Plantar will need 16 lbs of pecans and 24 lbs of walnuts to make a mix of 40 lbs. worth $4.80.
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10. 3. Eddie invested $2400 in two simple interest accounts
   3.   Eddie invested $2400 in two simple interest accounts. The annual rate in one account is 8% and the annual rate in the other is 11%. How much did he invest in each account if the annual interest totaled $240? P R
Int 8% x
.08
.08x
11% x
.11
.11(2400-x)
2400
240
.08x + .11(2400 – x) = 240
.08x x = 240
-.03x = 240
-.03x = - 24
x = 800, = 1600
Eddie invested $800 in the 8% account and $1600 in the 11% account.
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11. Principle Rate Interest 7% x .07 6% 12500- x .06 12,500 .06(12500-x)
Chazz Michael Michaels invested $12,500 in two simple interest accounts. One account earns annual simple interest of 7% while the other earns 6%. How much was invested at each rate if each account earned the same interest? Round your answer to the nearest dollar.
Principle
Rate
Interest 7% x
.07 6% x
.06
12,500
.07x
.06(12500-x)
To write the equation, the original problem states that the amount of interest is equal.
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13. 5. Bubba has two part time jobs. One pays $7
   5.   Bubba has two part time jobs. One pays $7.50 per hour and the other pays $9.00 per hour. Last week he earned $427 while working 50 hours. How many hours did he work at each job?
hours
rate
Total
Job 1 x
7.50
7.5x
Job 2
50- x
9.00
9(50 – x) 50
427
7.5x – 9x = 427
-1.5x = -23
x = 15 1/3 hours at Job 1 and 50 – 15 1/3 = 34 2/3 hours at Job 2
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14. 6. Kim had to pay $1200 in labor for some repairs to the house
 6. Kim had to pay $1200 in labor for some repairs to the house. The carpenter charged $18 an hour and the painter charged $15 per hour. If she paid for 73 hours of work, how much work was done by each?
hours
rate
Total
Painter x 15
15x
Carpenter
73- x 18
18(73 – x) 73
1200
18x + 15(73 – x) = 1200
18x – 15x = 1200
3x = 105
x = 35 hours for the carpenter
= 38 for the painter
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15. Investment
A man has $34,000 to invest. He invests some at 17% and the balance at 20%. His total annual interest income is $6245.
Find the amount invested at each rate.

16. Investment
A man has $34,000 to invest. He invests some at 17% and the balance at 20%. His total annual interest income is $6245.
Find the amount invested at each rate.
s = amount invested at 17%
How much is invested at 20%?

17. Investment
A man has $34,000 to invest. He invests some at 17% and the balance at 20%. His total annual interest income is $6245.
Find the amount invested at each rate.
s = amount invested at 17%
How much is invested at 20%?
If t is the 20% amount, then s + t = $34,000

18. Investment
A man has $34,000 to invest. He invests some at 17% and the balance at 20%. His total annual interest income is $6245.
Find the amount invested at each rate.
s = amount invested at 17%
If y is the 20% amount, then s + t = $34,000
Therefore, t = $34,000 - s

19. Investment s = amount invested at 17%
A man has $34,000 to invest. He invests some at 17% and the balance at 20%. His total annual interest income is $6245.
Find the amount invested at each rate.
s = amount invested at 17%
If y is the 20% amount, then s + t = $34,000
Therefore, t = $34,000 – s
Rate Amt Interest
17% .17
20% .20
Total $6245

20. Investment
A man has $34,000 to invest. He invests some at 17% and the balance at 20%. His total annual interest income is $6245.
Find the amount invested at each rate.
s = amount invested at 17%
If t is 20% amount, then s + t = $34,000
Therefore, t = $34,000 – s
Therefore .17 (s) (34,000 – s) = $6245

21. Investment
A man has $34,000 to invest. He invests some at 17% and the balance at 20%. His total annual interest income is $6245.
Find the amount invested at each rate.
s = amount invested at 17%
Therefore, t = $34,000 – s
.17 (s) (34,000 – s) = $6245
.17s s = 6245

22. Investment
A man has $34,000 to invest. He invests some at 17% and the balance at 20%. His total annual interest income is $6245.
Find the amount invested at each rate.
s = amount invested at 17%
Therefore, t = $34,000 – s
.17 (s) (34,000 – s) = $6245
.17s s = 6245
-.03s = - 555

23. Investment
A man has $34,000 to invest. He invests some at 17% and the balance at 20%. His total annual interest income is $6245.
Find the amount invest at each rate.
s = amount invested at 17%
Therefore, t = $34,000 – s
.17 (s) (34,000 – s) = $6245
.17s s = 6245
-.03s = - 555
s = 18, ,000 – 18,500 = 15,500

24. Check
A man has $34,000 to invest. He invests some at 17% and the balance at 20%. His total annual interest income is $6245.
Find the amount invest at each rate.
CHECK x = 18,500 ??
.17 · 18, · 15,500 = ??
= OK
Answer:
$18,500 at 17% and $15,500 at 20%.

25. Word Problems Involving Investments