Question

Anita’s and Casey’s bills do not vary from month to month. Anita pays $80 more than Casey does each month. Over the course of 4 months, their combined bills are $1,520.

Part A
Write the system of equations that describes this situation. Let a represent Anita's monthly payment and c represent Casey's monthly payment.

a +
c =


a =
+


Part B
Solve the system to find Anita’s and Casey’s monthly payments.

Anita: $
Casey: $

Answer 1

Casey's monthly payment is $150.
Anita's monthly payment is $230.

Explanation:

Part A:

The system of equations that describes this situation is:

a + c = Total monthly bill

a = c + 80

where a represents Anita's monthly payment, c represents Casey's monthly payment, and Total monthly bill represents the combined bills of Anita and Casey.

Part B:

To solve the system, we can substitute the second equation into the first equation and get:

(c + 80) + c = Total monthly bill

Simplifying this equation, we get:

2c + 80 = Total monthly bill

We also know that over the course of 4 months, their combined bills are $1,520. So we can write:

4(Total monthly bill) = 1520

Substituting the equation for Total monthly bill from the previous step, we get:

4(2c + 80) = 1520

Simplifying this equation, we get:

8c + 320 = 1520

Subtracting 320 from both sides, we get:

8c = 1200

Dividing both sides by 8, we get:

c = 150

So Casey's monthly payment is $150. To find Anita's monthly payment, we can use the second equation from Part A:

a = c + 80

a = 150 + 80

a = 230

Therefore, Anita's monthly payment is $230.