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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.

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  1. 2 May, 09:27
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    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
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