Question

Ms. Smith invested $22,000 in two accounts, one yielding 5% interest and the other yielding 9%. If she received a total of $1740 in interest at the end of the year, how much did she invest in each account?

Answer 1

I assume this is simple interest which is
\(I = prt\)
Here t = time = 1 year.

Let x be the amount invested at 5% and y be the amount invested at 9%.

The first equation represents the total amount invested:
\(x + y = 22000 \)

The second equation represents the interest earned:
\(5%x + 9%y = 1740\), or
\(0.05x + 0.09y = 1740\)

Solve the system of equations for x and y:
\(x + y = 22000 \)
\(0.05x + 0.09y = 1740\)

Answer 2

am i doing y=2200-x

Answer 3

then .09y=.05x-2740?

Answer 4

1740*

Answer 5

Careful, \(y = 22000 - x\)

Answer 6

Once you solve the first equation for y, then substitute what y is into the y of the second equation.

\(x + y = 22000\) ----> \(y = 22000 - x\)

\(0.05x + 0.09y = 1740\)

\(0.05x + 0.09(22000 - x) = 1740 \) Now solve this equation for x.

Answer 7

so i got x=6000

Answer 8

then i plug x back into x+y=22000 ?

Answer 9

Correct.

Answer 10

x is 5% & y is 9% ?

Answer 11

Look above. I wrote it down so we don't forget. It's in my first response.

Answer 12

got it. thank you!