Question

Nellie and her younger sister Debbie share expenses on a holiday. Nellie spends $122 more than Debbie. Their total expenses amount to $840.

A) Write a pair of linear equations to represent the information given above.

B)Explain how you can change this pair of equations to a linear equation in one unknown.

C)Apply your method to find how much Debbie spends on the holiday. Show your work.

Answer 1

see below

Explanation:

Let N = how much Nellie spends

Let D = how much Debbie spends

Part A

Nellie spends $122 more than Debbie.

N= D +122

Their total expenses amount to $840.

N+D =840

The two equations are

N= D +122

N+D =840

Part B

We can substitute the first equation which is solved for N into the second equation. Every place we see an N in the second equation, we replace it with D+122

Part C

N= D +122

N+D =840

(D+122) +D = 840

Combine like terms

2D +122 = 840

Subtract 122 from each side

2D+122-122=840-122

2D =718

Divide by 2

2D/2= 718/2

D =359

Debbie spends 359