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Setler79 [48]
3 years ago
14

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?
Mathematics
1 answer:
tresset_1 [31]3 years ago
8 0
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.




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