Beginning and Intermediate Algebra - Wallace Math Courses ...

− 0.06x − 0.06y = − 240 Add equations together
0.06x + 0.09y = 270
0.03y = 30 Divide both sides by 0.03
0.03 0.03
y = 1000 We have y, S1000 invested at 9%
x + 1000 = 4000 Plug into original equation
− 1000 − 1000 Subtract 1000 from both sides
x = 3000 We have x, S3000 invested at6%
S1000 at9% and S3000 at6% Our Solution
The same process can be used to find an unknown interest rate.
Example 190.
John invests S5000 in one account and S8000 in an account paying 4% more in
interest. He earned S1230 in interest after one year. At what rates did he invest?
Invest Rate Interest
Account1 5000 x
Account2 8000 x + 0.04
Total
Invest Rate Interest
Account1 5000 x 5000x
Account2 8000 x + 0.04 8000x + 320
Total
Invest Rate Interest
Account2 5000 x 5000x
Account2 8000 x + 0.04 8000x + 320
Total 1230
Our investment table. Use x for first rate
The second rate is 4% higher, orx+0.04
Be sure to write this rate asadecimal!
Multiply to fill in interest column.
Be sure to distribute 8000(x + 0.04)
Total interest was 1230.
5000x+8000x + 320 = 1230 Last column gives our equation
13000x + 320 = 1230 Combine like terms
− 320 − 320 Subtract 320 from both sides
13000x = 910 Divide both sides by 13000
13000 13000
x = 0.07 We have ourx,7% interest
(0.07)+0.04 Second account is 4% higher
0.11 The account with S8000 is at 11%
S5000 at7% and S8000 at 11% Our Solution
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