Question

A farmer bought a scratch ticket and found out later that he won $1,200,000. After 35% was deducted for income taxes he invested the rest; some at 3.5% and some at 5.75%. If the annual interest earned from his investments is $33,600, find the amount he invested at each rate.

Answer 1

The amount invested at 3.5% interest rate is $5,000.

The amount invested at 5.75% interest rate is $775,000.

What are the linear equations that represent the question?

Total amount invested = ( 1 -tax rate) x amount won

0.65 x 1,200,000 = $780,000

a + b = $780,000 equation 1

0.035a + 0.0575b = $33,600 equation 2

Where:

• a = amount invested at  3.5% interest rate
• b = amount invested at  5.75% interest rate

What are the amounts invested at  3.5% and 5.57% interest rate ?

Multiply equation 1 by 0.0575

0.0575a + 0.0575b = 44,850 equation 3

Subtract equation 2 from equation 3

11,250 = 2.25a

a = 11,250 / 2.25

a = $5000

In order to determine the value of b , subtract $5000 from 780,000.

780,000 - 5000 = $775,000

To learn more about simultaneous equations, please check: brainly.com/question/25875552

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