Word Problems InvolvingInvestments
Investment type problems are a type of mixtureproblem. In this type of problem we are mixingmoney into different accounts. For example…...
Ron Burgandy has $15,000 to invest. Heplans to diversify his money by investing itin two different accounts. One accountgives 11.5% interest and the other 9%interest. If he wants to make $1562.50 ininterest in the first year, how much shouldhe place in each account?
Ron Burgandy has $15,000 to invest. He plans to diversify hismoney by investing it in two different accounts. One accountgives 11.5% interest and the other 9% interest. If he wants tomake $1562.50 in interest in the first year, how much should heplace in each account?
.115
.09
x
15000 - x
The interest of the 2 accounts added together equal the total.
.115x
.09(15000-x)
15,000
1562.50
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. Howmany 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 walnutsthat will sell for $4.80 per pound. If the pecans cost $5.40 perpound and the walnuts cost $4.40 per pound, how many of eachshould he use?
3. Eddie invested $2400 in two simple interest accounts. Theannual rate in one account is 8% and the annual rate in the otheris 11%. How much did he invest in each account if the annualinterest totaled $240?
4. Fred and Irma invested $12,500 in two simple interestaccounts. One account earns annual simple interest of 7%while the other earns 6%. How much was invested at each rateif each account earned the same interest? Round your answerto the nearest dollar.
5. Bubba has two part time jobs. One pays $7.50 per hour andthe other pays $9.00 per hour. Last week he earned $427while working 50 hours. How many hours did he work at eachjob?
6. Kim had to pay $1200 in labor for some repairs to thehouse. The carpenter charged $18 an hour and the paintercharged $15 per hour. If she paid for 73 hours of work, howmuch work was done by each?
Mixture Solutions
1. 30 pounds of pecans
2. 16 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
6. 35 hours by the carpenter and 38 hours of work by the painter.
For complete details click to next slide.
162 + 5.4x = 6.48(x + 20)
162 + 5.4x = 6.48x + 129.6
162 = 6.48x – 5.4x + 129.6
162 – 129.6 = 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 tomake a mix worth $6.48
1. Mr. Planter wants to mix 20 lb of macadamia nuts that cost $8.10 perpound with pecans that cost $5.40 per pound. How many pounds of pecansshould 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)
5.4x + 4.4(40 – x) + = 40(4.8)
5.4x +176 – 4.4x + = 192
x + 176 = 192
x = 16
40 – x = 24
Mr. Plantar will need 16 lbs of pecans and 24 lbs of walnuts to make a mix of 40lbs. worth $4.80.
2. Mr. Planter also wants a 40 lb mixture of pecans and walnuts that willsell for $4.80 per pound. If the pecans cost $5.40 per pound and the walnutscost $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)
.08x + .11(2400 – x) = 240
.08x + 264 - .11x = 240
-.03x + 264 = 240
-.03x = - 24
x = 800, 2400-800= 1600
Eddie invested $800 in the 8% account and $1600 in the 11% account.
3. Eddie invested $2400 in two simple interest accounts. The annual ratein one account is 8% and the annual rate in the other is 11%. How much did heinvest in each account if the annual interest totaled $240?
P
R
Int
8%
x
.08
.08x
11%
2400 - x
.11
.11(2400-x)
2400
240
Chazz Michael Michaels invested $12,500 in twosimple interest accounts. One account earns annualsimple interest of 7% while the other earns 6%. Howmuch was invested at each rate if each account earnedthe same interest? Round your answer to the nearestdollar.
Principle
Rate
Interest
7%
x
.07
6%
12500- x
.06
12,500
.07x
.06(12500-x)
To write the equation, the original problemstates that the amount of interest is equal.
7.5x + 450 – 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
5. Bubba has two part time jobs. One pays $7.50 per hour and the otherpays $9.00 per hour. Last week he earned $427 while working 50 hours. Howmany 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
18x + 15(73 – x) = 1200
18x + 1095 – 15x = 1200
3x = 105
x = 35 hours for the carpenter
73- 35 = 38 for the painter
6. Kim had to pay $1200 in labor for some repairs to the house. The carpentercharged $18 an hour and the painter charged $15 per hour. If she paid for 73hours 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
Investment
A man has $34,000 to invest. He invests some at 17%and the balance at 20%. His total annual interestincome is $6245.
Find the amount invested at each rate.
Investment
A man has $34,000 to invest. He invests some at 17%and the balance at 20%. His total annual interest incomeis $6245.
Find the amount invested at each rate.
s = amount invested at 17%
How much is invested at 20%?
Investment
A man has $34,000 to invest. He invests some at 17%and the balance at 20%. His total annual interest incomeis $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
Investment
A man has $34,000 to invest. He invests some at 17% andthe 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
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
RateAmtInterest
17%.17
20%.20
Total$6245
Investment
A man has $34,000 to invest. He invests some at 17% and the balance at 20%. Histotal 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) + .20 (34,000 – s) = $6245
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) + .20 (34,000 – s) = $6245
.17s + 6800 - .2s = 6245
Investment
A man has $34,000 to invest. He invests some at 17% and thebalance 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) + .20 (34,000 – s) = $6245
.17s + 6800 - .2s = 6245
-.03s = - 555
Investment
A man has $34,000 to invest. He invests some at 17% and thebalance 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) + .20 (34,000 – s) = $6245
.17s + 6800 - .2s = 6245
-.03s = - 555
s = 18,50034,000 – 18,500 = 15,500
Check
A man has $34,000 to invest. He invests some at 17% and thebalance at 20%. His total annual interest income is $6245.
Find the amount invest at each rate.
CHECKx = 18,500 ??
.17 · 18,500 + .2 · 15,500 = 6245 ??
3145 + 3100 = 6245 OK
Answer:
$18,500 at 17% and $15,500 at 20%.
Word Problems InvolvingInvestments