Problema Solution
Jerry bought 4 times as many pencils as notebooks and spent a total of $21.60. He spent $2.40 more on the notebooks than pencils. Given that a notebook costs $3.20 more than a pencil, find the cost of a pencil.
Answer provided by our tutors
Let the cost of a pencil be $x
So, the cost of a notebook = $(x + 3.20)
If Jerry bought y notebooks, then he bought 4y pencils.
He spent $x * 4y = $4xy on pencils
He spent $(x + 3.20) * y = $(xy + 3.20y) on notebooks.
Now, xy + 3.20y - 4xy = 2.40
3.20y - 3xy = 2.40
3.20y = 3xy + 2.40
Also, 4xy + xy + 3.20y = 21.60
5xy + 3.20y = 21.60
5xy + 3xy + 2.40 = 21.60
8xy = 21.60 - 2.40
8xy = 19.20
xy = 19.20/8
xy = 2.40
So, 3.20y = 3xy + 2.40 = 3* 2.40 + 2.40 = 9.60
y = 9.60/3.20 = 3
So, x = 2.40/y = 2.40/3 = 0.80
The cost of a pencil is $0.80