Question

5. Una persona invierte en un producto una cantidad de dinero, obteniendo un 5% de beneficio. Por otra inversión en un segundo producto, obtiene un beneficio del 3,5%. Sabiendo que en total invirtió 10 000 y que los beneficios de la primera inversión superan en 330 a los de la segunda, ¿cuánto dinero invirtió en cada producto?

Answer 1

A person invests a quantity of money in a product, obtaining a 5% profit. For another investment in a second product, he gets a profit of 3.5%. Knowing that in total he invested $10,000 and that the benefits of the first investment are $330 in excess of those of the second, how much money did you invest in each product?

Answer: first product = $8,000 , second product= $2,000✔️

Let A and B be the amounts invested in each product.

A + B = $10,000 } (I)

A·5/100 = B·3.5/100 + $330 } (II)

(5A - 3.5B)/100 = $330

5A - 3.5B = 100·$330

From (I) we have: A = $10,000 - B } (I)

5($10,000 - B) - 3.5B = $33,000

$50,000 - 5B -3.5B = $33,000

$50,000 - $33,000 = 5B + 3.5B

$17,000 = 8.5B

B = $17,000/8.5 = $2,000 , Investment second product

A = $10,000 - B } (I)

A = $10,000 - $2,000 = $8,000 , investment first product

Answer: first product = $8,000 , second product= $2,000✔️

Verify

Benefit first amount = $8,000 · 5/100 = $400

Benefit second amount = $2,000 · 3.5/100 = $70

Excess = $400 - $70 = $330✔️checked!

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