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.

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

tickets for the harlem globetrotters

show at michigan state university in

2010 cost $16, $23, or, for vip seats, $40.

total revenue = 16x + 23y + 40z

if 9 times as many $16 tickets were sold

as vip tickets,

x = 9z => x – 9z = 0, if 9 times as many $16 tickets were sold

as vip tickets,

x = 9z => x – 9z = 0, sales of all three kinds of tickets would

total $46,575.

16x + 23y + 40z = 46575, how many of each kind of ticket would

have been sold?

solve for x, y and z

x − 9z = 0

x − y − z = 55

16x + 23y + 40z = 46575

x = 1170

y = 985

z = 130

welcome!

8

step-by-step explanation: