Q:

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.

Accepted Solution

A:
Answer:see belowStep-by-step explanation:Let N = how much Nellie spendsLet D = how much Debbie spendsPart ANellie spends $122 more than Debbie.N= D +122 Their total expenses amount to $840. N+D =840The two equations areN= D +122N+D =840Part BWe 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+122Part CN= D +122N+D =840(D+122) +D = 840Combine like terms2D +122 = 840Subtract 122 from each side2D+122-122=840-1222D =718Divide by 22D/2= 718/2D =359Debbie spends 359