A student bought 3 boxes of pencils and 2 boxes of pens for $6. He then bought 2 boxes of pencils and 4 boxes of pens for $8. Find the cost of each box of pencils and each box of pens.
Pencils: $1.00
Pens: $1.50
To solve this problem, we can use a system of equations. Let's denote the cost of each box of pencils as "x" and the cost of each box of pens as "y".
From the information given, we can create two equations:
Equation 1: 3x + 2y = 6
Equation 2: 2x + 4y = 8
To find the cost of each box of pencils and each box of pens, we need to solve this system of equations.
We can start by multiplying Equation 1 by 2 and Equation 2 by 3 to eliminate the variable x.
Equation 1 multiplied by 2:
6x + 4y = 12
Equation 2 multiplied by 3:
6x + 12y = 24
Next, we can subtract Equation 1 multiplied by 2 from Equation 2 multiplied by 3 to eliminate x.
(6x + 12y) - (6x + 4y) = 24 - 12
8y = 12
Now, divide both sides of the equation by 8 to solve for y.
y = 12/8
y = 3/2
y = 1.5
So, the cost of each box of pens is $1.50.
Substitute this value of y into Equation 1 to solve for x:
3x + 2(1.5) = 6
3x + 3 = 6
3x = 6 - 3
3x = 3
x = 3/3
x = 1
So, the cost of each box of pencils is $1.
Therefore, each box of pencils costs $1 and each box of pens costs $1.50.