Precalculus Question

Question

Noah invests $5100 in two different accounts. The first account paid 9%, the second account paid 6% in interest. At the end of the first year he had earned $375 in interest. How much was in each account?

Answer 1

$2300 at 9%

$2800 at 6%

A system of two equations in two unknowns, x and y will work here.

Equation 1 for the total amount invested

x + y = 5100

Equation 2 for the total interest earned

0.09x + 0.06y = 375

I will use Equation 1 and Substitution below to solve for the unknowns

Equation 1

x + y = 5100

So

y = 5100 -x

Substitute the quantity above in Equation 2 to solve for x

Equation 2

0.09x + 0.06y = 375

0.09x + 0.06(5100 -x) = 375

0.09x + 306 - 0.06x = 375

Combine like terms

0.03x + 306 = 375

Subtract 306 from both sides of the equation

0.03x = 69

Divide both sides of the equation by 0.0e

x = 23000

y = 5100 -x = 5100 - 2300 = 2800

Checking in Equation 2

0.09x + 0.06y = 375

0.09(2300) + 0.06(2800) = 375

207 + 168 = 375

375 = 375

Of course there other ways to do this but I hope you find this information useful, if you have any questions, send me a message.