Question

Barbara wants to earn $500 a year by investing $5000 in two
accounts, a savings plan that pays 8% annual interest and a highrisk
option that pays 13.5% interest. How much should she invest
at 8% and how much at 13.5%? Write a system of equations that
would allow you to solve Barbara’s dilemma.

Answer 1

Solutions 

Let x = amount invested at 8%. 

Let y = amount invested at 13.5%. 

It is given that the total invested in both accounts is $5000. The equation that represents this info is: x + y = 5000. It is also given that the total amount earned from both accounts is $500. The amount earned in the 8% account will be the amount invested times the rate: 0.08x And the amount earned in the 13.5% account will be: 0.135y 

Together the two accounts will total $500 earned. The equation will be: 0.08x + 0.135y = 500. Solving this system of 2 equations would give both account values. 

Answer 2

Given: 

1. Barbara invested $5000 and she wants to earn $500

Need to find out:

The system of equation

Solution:

Let us assume the 8% as X

Let us assume the 13.5% as Y 

⇒ X + Y = $5000 ( according to question )

The amount she wants’ to earn in the both situation is 500

By this we can say -

8% would be 0.08x

13.5% would be 0.135y

0.08x + 0.135y = 500 (here we are using 500 because the amount she wants’ is 500)

∴ The system of equation will be "0.08x + 0.135y = 500"