Question

Amy purchased 17 pencils and 18 pens for a fund-raiser at school and spent $61.50. jocelyn purchased 10 pencils and 21 pens and spent $57. how much does each pencil cost? (1 point) $2.00 $1.50 $1.25 $1.00

Answer 1

Answer: $1.50

Work Shown

x = cost of 1 pencil in dollars

y = cost of 1 pen in dollars

17x+18y = cost of 17 pencils and 18 pens

17x+18y = 61.50 is one equation to set up

The other equation would be 10x+21y = 57

We have this system of equations

`\begin{cases}17x+18y = 61.50\\10x+21y = 57\end{cases}`

Multiply both sides of equation (1) with the value -21.

Multiply both sides of equation (2) with the value 18

We get this equivalent system of equations

`\begin{cases}-357x-378y = -1291.50\\180x+378y = 1026\end{cases}`

Add the terms straight down.

• The x terms combine to -357x+180x = -177x
• The y terms combine to -378y + 378y = 0y = 0, meaning the y terms go away.
• The right hand sides combine to -1291.50+1026 = -265.50

We then have:

-177x = -265.50

x = -265.50/(-177)

x = 1.50 dollars is the cost of one pencil