Question

Mrs. Ellis is shopping for school

supplies with her children. Hansen
selected 3 one-inch binders and 2 two-
inch binders, which cost a total of $20.
Pam selected 3 one-inch binders and 5
two-inch binders, which cost a total of
$32. How much does each size of
binder cost?

Answer 1

Each one-inch binder costs $2.67 and each two-inch binder costs $6.

Explanation:

Let's call the cost of a one-inch binder "x" and the cost of a two-inch binder "y".

From Hansen's purchase, we know that 3x + 2y = $20.

From Pam's purchase, we know that 3x + 5y = $32.

We can use these two equations to solve for the cost of each size of binder. If we subtract the first equation from the second, we get:

2y = $32 - $20 = $12

So, y = $6, which is the cost of a two-inch binder.

Next, we can plug this value back into either of the original equations to find the cost of a one-inch binder:

3x + 2($6) = $20

Expanding the right side, we get:

3x + $12 = $20

Subtracting $12 from both sides, we get:

3x = $8

Finally, dividing both sides by 3, we find that:

x = $2.67

So, each one-inch binder costs $2.67 and each two-inch binder costs $6.

Answer 2

Let's call the cost of a one-inch binder "x" and the cost of a two-inch binder "y".

From the first piece of information, we know that 3 one-inch binders and 2 two-inch binders cost a total of $20:

3x + 2y = 20

From the second piece of information, we know that 3 one-inch binders and 5 two-inch binders cost a total of $32:

3x + 5y = 32

We now have two equations with two unknowns, x and y. We can solve for one of the unknowns by using either of the two equations and then substituting the result into the other equation.

Let's solve for x by rearranging the first equation:

x = (20 - 2y) / 3

Now we can substitute this expression for x into the second equation:

3((20 - 2y) / 3) + 5y = 32

Expanding and simplifying the left-hand side:

20 - 2y + 15y = 32

13y = 12

Finally, solving for y:

y = 12 / 13

So, each two-inch binder costs $12 / 13 = $0.92. And finally, we can use either equation to find the cost of a one-inch binder:

x = 20 - 2y = 20 - 2($0.92) = $1.08

So, each one-inch binder costs $1.08