Financial Mixture problem help

Question

Ethan has a total college account of $175,000. He is going to split this into two different funds, one which pays 6.5% and the other that pays 8%. How much should he put in each account so that he gets the $12,000 in interest per year that he needs to pay for college?

Answer 1

Hello Lex,

Let X = amount put into the 8.0% interest bearing account

Let Y = amount put into the 6.5% interest bearing account

X + Y = 175,000

X = 175,000 - Y

Y = 175,000 - X

We can express the mixture problem with the following equation:

(0.065)(175,000 - X) + (0.08)(175,000 -(175,000 - X)) = 12,000

11,375 - 0.065X + 0.08X = 12,000

11,375 + 0.015X = 12,000

.015X = 625

X = 625/0.015

X = 41,666.67

Y = 175,000 - 41,666.67 = 133,333.33

By plugging in the X and Y values, we are able to satisfy the equation.

(0.065)(133,333.33) + (0.08)(41,666.67) = 12,000