Susan Marciano invested part of her $37,000 bonus in a fund that paid a 12% profit and invested the rest in stock that suffered a 5% loss. find the amount of each investment if her overall net profit was $3,420

Question

Gunner Chang

Mathematics

9 December, 22:58

Susan Marciano invested part of her $37,000 bonus in a fund that paid a 12% profit and invested the rest in stock that suffered a 5% loss. find the amount of each investment if her overall net profit was $3,420

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Answers (1)

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Twig · Answer 1

The amount invested in funds that earned 12% profit is 31000

The amount invested in stock that suffered 5% loss is 6,000.

Step-by-step explanation:

Let x be the amount invested in funds that earned 12%.

Then the amount invested in stock that suffered 5% loss is 37000 - x.

The profit from investment in funds is = 12% of x

= 0.12·x

The loss from investment in stock is = 5% of (37000 - x)

= 0.05 * (37000 - x)

The net profit is 0.12·x - 0.05 * (37000 - x)

As the net profit given in the problem is $3420, we have:

0.12·x - 0.05 * (37000 - x) = 3420

Solving for x, we have:

12·x - 5 * (37000 - x) = 342000 (multiply both sides by 100)

12·x - 185000 + 5·x = 342000

17·x = 527000

⇒ x = 31000

Hence, The amount invested in funds that earned 12% profit is 31000 and the amount invested in stock that suffered 5% loss is 37000 - x = 37000 - 31000 = 6,000.