# The percent 2

The percent return rate of a growth fund, income fund, and money market are 10%, 7%, and 5%, respectively. Suppose you have 3200 to invest and want to put twice as much in the growth fund as in the money market to maximize your return. How should you invest in getting a return of 250 dollars in 1 year?

a =  1300
b =  1250
c =  650

## Step-by-step explanation:

3200 = a+b+c
250 = (a·0.10 + b·0.07+c·0.05)
a = 2c

3200 = a+b+c
250 = (a·0.10 + b·0.07+c·0.05)
a = 2·c

a+b+c = 3200
0.1a+0.07b+0.05c = 250
a-2c = 0

Row 2 - 0.099999999999994 · Row 1 → Row 2
a+b+c = 3200
-0.03b-0.05c = -70
a-2c = 0

Row 3 - Row 1 → Row 3
a+b+c = 3200
-0.03b-0.05c = -70
-b-3c = -3200

Pivot: Row 2 ↔ Row 3
a+b+c = 3200
-b-3c = -3200
-0.03b-0.05c = -70

Row 3 - -0.03/-1 · Row 2 → Row 3
a+b+c = 3200
-b-3c = -3200
0.04c = 26

c = 26/0.04 = 650
b = -3200+3c/-1 = -3200+3 · 650/-1 = 1250
a = 3200-b-c = 3200-1250-650 = 1300

a = 1300
b = 1250
c = 650

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