Question

Liam deposits I dollars into an account that earns 0.9% in simple interest each year. Grace

deposits g dollars into an account that earns 1.1% in simple interest each year. Both Liam and
Grace let their money earn interest for one year and make no further deposits. If Liam's initial
deposit was $800 more than Grace's, and if both Liam and Grace earn the same amount of
interest after one year, which of the following systems of equations could be used to find their
initial deposits?

Answer 1

1. Liam's initial deposit was $2694.74 and Grace's initial deposit was $1894.74. 2. The system of equations that could be used to find their initial deposits is: I = g + 800, 0.009I = 0.011g

Explanation:

Let's first use the formula for simple interest to find the interest earned by Liam and Grace after one year:

Interest earned by Liam = I x 0.009

Interest earned by Grace = g x 0.011

We also know that both Liam and Grace earn the same amount of interest after one year, so:

I x 0.009 = g x 0.011

We also know that Liam's initial deposit was $800 more than Grace's, so:

I = g + 800

Now we can substitute I in the first equation:

(g + 800) x 0.009 = g x 0.011

Simplifying and rearranging:

0.0072g + 7.2 = 0.011g

0.0038g = 7.2

g = 1894.74

Now we can find I:

I = g + 800

I = 1894.74 + 800

I = 2694.74

Therefore, Liam's initial deposit was $2694.74 and Grace's initial deposit was $1894.74.

The system of equations that could be used to find their initial deposits is:

I = g + 800

0.009I = 0.011g

Hope this helps! If you need more help, ask me! :]

Sorry if it's wrong.