Question

Last summer Olivia earned $3800 by selling cakes. She invested some of the money in a savings account that paid 4.5%/yr and the rest in a government bond that paid 5.5%/yr. After one year, she has earned $180 in interest. How much did she invest at each rate? [4]

Answer 1

Olivia invested $2900 in a savings account that paid 4.5%/yr and $900 in a government bond that paid 5.5%/yr.

Explanation:

With the information provided you can write the following equations:

x+y=3800 (1)

0.045x+0.055y=180 (2), where:

x is the amount invested in a savings account

y is the amount invested in a government bond

First, you can solve for x in (1):

x=3800-y (3)

Next, you can replace (3) in (2) and solve for y:

0.045(3800-y)+0.055y=180

171-0.045y+0.055y=180

0.01y=9

y=9/0.01

y=900

Finally, you can replace the value of y in (3) to find x:

x=3800-900

x=2900

According to this, the answer is that Olivia invested $2900 in a savings account that paid 4.5%/yr and $900 in a government bond that paid 5.5%/yr.