Question

Kyra had $20,000 to invest. She decided to put the money into three different aCounts earning 3%, 5%, and 7%

simple interest respectively, and she earned a total of $920.00 in interest. She invested half as much money at 7%
as at 3%. How much did she invest in each aCount?
a. Write a system of equations that models this situation.
b. Find the amount invested in each aCount

Answer 1

$8000, $4000 and $8000.

Explanation:

Let the amount invested in 3%, 5% and 7% simple interest are a, b and c.

Given that, she invested half as much money at 7% as at 3%.

so, c=a/2, ⇒ a=2c. ...... (1)

Now, a+b+c =20000 ........ (2), ⇒3c+b =20000 {From equation (1)}......... (3)

She earned as interest a total of $920.

Hence, 3a/100+5b/100+7c/100 =920

⇒ 3a+5b+7c =92000

⇒13c +5b =92000 {From equation (1)} ..... (4)

Solving equations (4) and (3), we get 13a+5(20000-3c) =92000

2c = 8000

⇒ c= 4000. then a= 2c =8000

Again from equation (2), b=20000-4000-8000=8000

Therefore, the amount invested in the three accounts are $8000, $4000 and $8000. (Answer)