Someone plz help been stuck on this question for the last 2 hours



Paul has $30,000 to invest. His intent is to earn 11% interest on his investment. He can invest part of his money at 7% interest and part at 13% interest. How much does Paul need to invest in each option to make a total 11% return on his $30,000?
7% interest =$?

13% interest =$?

Answer:

7% interest = $10000

13% interest = $20000

Step-by-step explanation:

Let the amount invested at 7% interest be x.

Let the amount invested at 13% interest be y.

Thus;

x + y = 30000 - - - (eq 1)

We want to find out how much Paul needs to invest in each option to make a total 11% return on his $30,000.

Thus;

0.07x + 0.13y = 0.11(30000)

Multiply through by 100 to get rid of the decimal;

7x + 13y = 0.11(30000 × 100).

7x + 13y = 330000 - - - (eq 2)

From eq 1, x = 30000 - y

Put this for x in eq 2 to get;

7(30000 - y) + 13y = 330000

210000 - 7y + 13y = 330000

6y = 330000 - 210000

6y = 120000

y = 120000/6

y = $20000

x = 30000 - 20000

x = $10000

Thus;

Amount invested at;

7% interest = $10000

13% interest = $20000

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