The cost of a pencil is $0.25 more than the cost of an eraser. If the cost of 8 pencils and 10 erasers is $12.80, find the cost of each.
cost of eraser --- x cents
cost of pencil --- x+25 cents
8(x+25) + 10x = 1280
solve for x and state your conclusion
Let's assume the cost of an eraser is x dollars.
According to the given information, the cost of a pencil is $0.25 more than the cost of an eraser. Therefore, the cost of a pencil would be x + $0.25.
Given that the cost of 8 pencils and 10 erasers is $12.80, we can form an equation:
8(x + $0.25) + 10x = $12.80
Simplifying the equation:
8x + $2 + 10x = $12.80
18x + $2 = $12.80
18x = $12.80 - $2
18x = $10.80
Dividing both sides of the equation by 18 to find the value of x:
x = $10.80 รท 18
x = $0.60
The cost of an eraser is $0.60.
Substituting the value of x into the equation for the cost of a pencil:
Pencil cost = x + $0.25
Pencil cost = $0.60 + $0.25
Pencil cost = $0.85
Therefore, the cost of each eraser is $0.60 and the cost of each pencil is $0.85.
To find the cost of each pencil and eraser, we can set up a system of equations based on the given information.
Let's assume the cost of an eraser is x (in dollars).
According to the given information, the cost of a pencil is $0.25 more than the cost of an eraser. So, the cost of a pencil would be x + $0.25.
Now, we can set up the equations based on the number of pencils and erasers:
Equation 1: 8 pencils + 10 erasers = $12.80
Equation 2: Cost of 1 pencil = x + $0.25
Now, let's solve the system of equations to find the cost of each item.
From Equation 1: 8 pencils + 10 erasers = $12.80
Rewriting it: 8(x + $0.25) + 10x = $12.80
Expanding: 8x + $2 + 10x = $12.80
Combining like terms: 18x + $2 = $12.80
Subtracting $2 from both sides: 18x = $12.80 - $2
Calculating: 18x = $10.80
Dividing both sides by 18: x = $10.80 / 18
Calculating: x = $0.60
So, the cost of one eraser is $0.60.
Now, let's find the cost of one pencil using Equation 2.
Cost of 1 pencil = x + $0.25
Substituting the value of x: Cost of 1 pencil = $0.60 + $0.25
Calculating: Cost of 1 pencil = $0.85
Therefore, the cost of each pencil is $0.85, and the cost of each eraser is $0.60.