The ratio of the number of pencils to the number of pens John bought was 3:2. Each pen cost $9 while each pencil cost 1/3 as much as a pen. He paid a total of $108 for all of them. How much more did John spend on the pens than on the pencils?

Question

The ratio of the number of pencils to the number of pens John bought was 3:2. Each pen cost $9 while each pencil cost 1/3 as much as a pen. He paid a total of $108 for all of them. How much more did John spend on the pens than on the pencils?

Answer 1

X - number of pencils $3

Y - number of pens $9

3X + 9Y = 108 => X + 3Y = 36 (1)

X/Y = 3/2 => 2X = 3Y (2)

Substitute 3Y in (1):

X + 2X = 36

X = 12 pencils

12*3 = $36 he spent on the pencils

108 - 36 = $72 he spent on the pens