Justin is looking at two accounts in which to invest his money. If he invests $25,000 in the first account and $5000 in the second account, then his total investment of $30,000 will receive $1700 in interest at the end of one year. If he invests $27,000 in the first account and 3000 in the second account, then his total investment of $30,000 will receive $1620 in interest at the end of one year.
For each account, what percentage of the investment is received in interest after one year?

Question

Justin is looking at two accounts in which to invest his money. If he invests $25,000 in the first account and $5000 in the second account, then his total investment of $30,000 will receive $1700 in interest at the end of one year. If he invests $27,000 in the first account and 3000 in the second account, then his total investment of $30,000 will receive $1620 in interest at the end of one year.
For each account, what percentage of the investment is received in interest after one year?

hero · Answer

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hero · Answer

1. Set Up Variables

x = 1st account percent interest 
y = 2nd account percent interest

2. Setup Equations

1st Possibility
Total interest received = 25,000x + 5,000y = 1700

2nd Possibility: 
Total interest received = 27,000x + 3000y = 1620

3. Solve System Of Equations
25,000x + 5000y = 1700
27,000x + 3000y = 1620

(a) Isolate y in both equations: 
y = (1700 - 25,000x)/5000
y = (1620 - 27,000x)/3000

(b) Set y = y and cross-multiply: 
3000(1700 - 25,000x) = 5000(1620 - 27,000x)

(c) Reduce both fractions by factor of 1/100: 
30(17 - 250x) = 50(16.20 - 270x)

(d) Continue solving for x: 
510 - 7500x = 810 - 13500x
13500x - 7500x = 810 - 510
6000x = 300
x = 300/6000
x = 3/60
x = 1/20
x = .05

4. Substitute x back into one of the original equations to find y: 
y = .09

5. Solution: 
Therefore, for each account, after one year, the percent investment received will be 5% and 9% respectively.