Question

Shireen decided to deposit her graduation gift money in two different savings accounts. Account X has an interest rate of .5% and Account Y has an interest rate of .25%. Altogether, she received $5000 from graduation. If after the first year Her interest earned was $21.25, how much was deposited into each account?a. Define your variables by assigning them to the real-world quantities in the problem.b. Write a system of equations in standard form you can use to solve for those quantities.c. Calculate the x and y intercepts for both equations.d. How much was deposited in each account? Use whatever method you want to solve thesystem of equations.

Answer 1

Let x= be the amount in the account with .5%

Let y be the amount in the account with .25%

We know that interest is

I = PRT

I = 21.25 and time is 1 year so t=1

I = x(.005)(1) + y (.0025)

We also know that the amount invested is 5000

x+y = 5000

The system of equations is

21.25 = .005x + .0025y

x+y = 5000

21.25 = .005x+.0025y

Let x = 0

21.25 = .0025y

21.25/.0025 =y

The y intercept is 8500

Let y =0

21.25 = .005x

21.25/.005 =x

The x intercept is 4250

x+y = 5000

Let x = 0

The y intercept is 5000

Let y =0

The x intercept is 5000

Using substitution

x = 5000-y

21.25 = .005(5000-y) + .0025y

21.25 = 25 - .005y +.0025y

21.25-25 = -.0025y

-3.75 = -.0025y

-3.75/-.0025 = y

1500 = y

Now find x

x+y = 5000

x+1500=5000

x = 5000-1500

x = 3500