Peter has $2000 to invest. Part of the money is to be invested at 6% and the rest at 7%. How much is invested in each account if the total interest in a year is $135?

Question

John has $2000 to invest. Part of the money is to be invested at 6% and the rest at 7%. How much is invested in each account if the total interest in a year is $135?

pls assist!

Answer 1

Hi Jessica A.

$500 was invested at 6%

1500 was invested at 7%

You can use a system of equations to solve for the amounts, with Equation 1 for the total amount invested and Equation 2 for the total interest earned in a year

Let x = amount invested at 6%

Let y = amount invested at 7%

Since the amount invested is 2000, then

Equation 1

x + y = 2000

and y = 2000 -x

Since the total interest earned for 1 year is 135 then

Equation 2

.06x + .07y = 135

You can make a substitution for y based on the first equation which puts everything in terms of x

0.06x + 0.07(2000 - x) = 135

0.06x + 140 - 0.07x = 135

Combine like terms

0.06x - 0.07x + 140 = 135

-0.01x + 140 = 135

Subtract 140 from both sides of the equation

-0.01x = -5

Divide both sides of the equation by -0.01

x = 500

We know from Equation 1 that y = 2000 - x

y = 2000 - 500 = 1500

I hope this helps you can check the values in both equations.