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,
[tex]10x+21( \frac{61.50-17x}{18} )=57[/tex]
[tex]10x+7( \frac{61.50-17x}{6} )=57[/tex]
[tex]10x+ \frac{430.50-119x}{6}=57[/tex]
[tex]10x* \frac{6}{6} + \frac{430.50-119x}{6}=57[/tex]
[tex]\frac{60x}{6} + \frac{430.50-119x}{6}=57[/tex]
[tex]\frac{430.50+60x-119x}{6}=57[/tex]
[tex]430.50-59x=57*6[/tex]
[tex]430.50-59x=342[/tex]
[tex]59x=430.50-342[/tex]
[tex]x=\frac{88.5}{59} [/tex]
[tex]x=1.5[/tex]
Now,
Substituting the value of "x" in equation (3), we get,
[tex]y =\frac{61.50-17x}{18} [/tex]
[tex]y =\frac{61.50-17(1.5)}{18} [/tex]
[tex]y =\frac{61.50-22.5}{18} [/tex]
[tex]y =\frac{39}{18} [/tex]
[tex]y =2.17[/tex]
[tex]y =2[/tex] approx. (rounded)
So, Each pencil costs $1.5 and each pen costs $2.
