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.

Question

Mathematics

Rebecca Waller

12 May, 18:21

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.

+3

Answers (1)

Know the Answer?

Phoenix Mullins · Answer 1

see below

Step-by-step 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