Question

Mrs. Martinez has $10,000 to invest. One bank offers her a return of 7.5% on the whole sum. Another bank offers her a return of 8% on part of the sum, and 6% on the rest of the sum. How much of the $10,000 would need to be invested at 8% at the second bank, for the overall return to be the same as at the first bank?

Answer 1

x = $7,500

Explanation:

0.08x + 0.06($10,000 - x) = $750

0.08x + $600 - 0.06x = $750

0.02x = $750 - $600

0.02x = $150

x = $150 / 0.02

x = $7,500

Answer 2

Explanation:

Let's assume Mrs. Martinez invests x dollars at 8% interest at the second bank. The remaining amount, $10,000 - x, would then be invested at 6% interest.

To calculate the overall return, we need to equate the returns from both investments.

Return from the first bank at 7.5%: (7.5/100) * $10,000 = $750

Return from the second bank at 8% on x dollars: (8/100) * x

Return from the second bank at 6% on ($10,000 - x) dollars: (6/100) * ($10,000 - x)

To make the overall returns equal, we can set up the following equation:

(8/100) * x + (6/100) * ($10,000 - x) = $750

Simplifying the equation:

0.08x + 0.06($10,000 - x) = $750

0.08x + $600 - 0.06x = $750

0.02x = $750 - $600

0.02x = $150

x = $150 / 0.02

x = $7,500

Mrs. Martinez would need to invest $7,500 at 8% interest at the second bank to achieve the same overall return as the first bank.