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?

Answer 1

Each pencil costs $1.50 and each pen costs $2.00

Explanation:

Answer 2

Let,
pencils be "x"
pens be "y"

According to the question,
17x + 18y = 61.50 ----------> equation (1)
10x + 21y = 57 -----------------> equation (2)

Now,
Taking equation (1),
17x + 18y = 61.50
18y = 61.50 - 17x
y = (61.50 - 17x ) / 18 -----> equation (3)

Now, substituting the value of "y" in equation (2), we get,


`10x+21( (61.50-17x)/(18) )=57`


`10x+7( (61.50-17x)/(6) )=57`


`10x+ (430.50-119x)/(6)=57`


`10x* (6)/(6) + (430.50-119x)/(6)=57`


`(60x)/(6) + (430.50-119x)/(6)=57`


`(430.50+60x-119x)/(6)=57`


`430.50-59x=57*6`


`430.50-59x=342`


`59x=430.50-342`


`x=(88.5)/(59)`


`x=1.5`

Now,
Substituting the value of "x" in equation (3), we get,


`y =(61.50-17x)/(18)`


`y =(61.50-17(1.5))/(18)`


`y =(61.50-22.5)/(18)`


`y =(39)/(18)`


`y =2.17`


`y =2` approx. (rounded)

So, Each pencil costs $1.5 and each pen costs $2.