help! I’m confused on how to solve this equation.

Question

A farmer bought a scratch ticket and found out later that he won $500,000. After 30% was deducted from income taxes he invested the rest; some at 3.5% and some at 5.25%. If the annual interest earned from his investments is $15,575, find the amount he invested at each rate.

Answer 1

.7(500,000) = 350,000 after taxes

.0525x + .035(350,000-x) = 15,575

(.0175)x = 15,575- 12,250 = 3,325

x = 3,325/.0175 = $190,000 invested at 5.25%

350,000-190,000 = $160,000 invested at 3.5%

.035(160) + .0525(190) = 5.6 + 9.975 = 15.575

15,575/350,000 = 4.45% average return on both investments

3.5 is within .95 of 4.45

5.25 is within .8 of 4.45 so you know you need more invested at 5.25% than at 3.5%

.95/.8 = 1.1875 times more invested at 5.25%

1.1875 x 160 =190