MATH SOLVE

4 months ago

Q:
# Ernie deposited $4000 between two savings accounts. One account paid 4% simple interest and the other paid 2%. At the end of one year, Ernie had earned $140 in interest for both accounts. How much money did Ernie deposit in the account that paid 4% interest?

Accepted Solution

A:

Let x represent the amount of $ in the 4% account and y in the 2% account.

Then x + y = $4000 (total savings).

Interest at 4% would be x*0.04*1 = 0.04x, and

Interest at 2% would be y*0.02*1 = 0.02y.

Then 0.04x + 0.02y = $140 interest, total.

We must solve this system of linear equations.

Mult. 0.04x + 0.02y = $140 by 100 to remove the fractions:

4x + 2y = $14000 We already know that x + y = $4000, so y = $4000-x.

Then 4x + 2y = $14000 becomes 4x + 2($4000-X) = $56000.

Simplifying, 4x + $8000 - 2x = 14000.

2x = $6000

x = $3000 at 4%

y = $1000 at 2%

Then x + y = $4000 (total savings).

Interest at 4% would be x*0.04*1 = 0.04x, and

Interest at 2% would be y*0.02*1 = 0.02y.

Then 0.04x + 0.02y = $140 interest, total.

We must solve this system of linear equations.

Mult. 0.04x + 0.02y = $140 by 100 to remove the fractions:

4x + 2y = $14000 We already know that x + y = $4000, so y = $4000-x.

Then 4x + 2y = $14000 becomes 4x + 2($4000-X) = $56000.

Simplifying, 4x + $8000 - 2x = 14000.

2x = $6000

x = $3000 at 4%

y = $1000 at 2%