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

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,

$10x+21( \frac{61.50-17x}{18} )=57$

$10x+7( \frac{61.50-17x}{6} )=57$

$10x+ \frac{430.50-119x}{6}=57$

$10x* \frac{6}{6} + \frac{430.50-119x}{6}=57$

$\frac{60x}{6} + \frac{430.50-119x}{6}=57$

$\frac{430.50+60x-119x}{6}=57$

$430.50-59x=57*6$

$430.50-59x=342$

$59x=430.50-342$

$x=\frac{88.5}{59}$

$x=1.5$

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

$y =\frac{61.50-17x}{18}$

$y =\frac{61.50-17(1.5)}{18}$

$y =\frac{61.50-22.5}{18}$

$y =\frac{39}{18}$

$y =2.17$

$y =2$   approx. (rounded)

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