## Susan invests 2 times as much money at 9% as she does at 5%. If her total interest after 1 year is \$1380, how much does she have invested at

Question

Susan invests 2 times as much money at 9% as she does at 5%. If her total interest after 1 year is \$1380, how much does she have invested at each rate?

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2 weeks 2021-09-07T21:33:44+00:00 1 Answer 0

## Answers ( )

1. Answer: She invested \$12000 at 9% and \$6000 at 5%

Step-by-step explanation:

Let x represent the amount which she invested in the account paying 9% interest.

Let y represent the amount which she invested in the account paying 5% interest.

Susan invests 2 times as much money at 9% as she does at 5%.. This means that

x = 2y

The formula for determining simple interest is expressed as

I = PRT/100

Considering the account paying 9% interest,

P = \$x

T = 1 year

R = 9℅

I = (x × 9 × 1)/100 = 0.09x

Considering the account paying 5% interest,

P = \$y

T = 1 year

R = 5℅

I = (y × 5 × 1)/100 = 0.05y

If her total interest after 1 year is \$1380, it means that

0.09x + 0.05y = 1380 – – – – – – – – – -1

Substituting x = 2y into equation 1, it becomes

0.09 × 2y + 0.05y = 1380

0.18y + 0.05y = 1380

0.23y = 1380

y = 1380/0.23

y = 6000

x = 2y = 2 × 6000

x = 12000