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Pencil Set

Pencil Set

if 1backpack and 2pencil sets cost $22.25 and 2backpacks and 1 pencil set cost$37.00 how much is each item?

When dealing with unknowns it is important to first make sure that the problem is solvable. For the number of unknowns you must have the same or greater number of variables. In this problem we have two unknowns: price of backpacks, and price of pencil sets; we also have two equations to solve them so it is possible.

Let us make the price of a backpack = bp and the price of a pencil set = ps. Our equations given from the problem would be as follows:

1 bp + 2 ps = 22.25
and
2 bp + 1 ps = 37.00

Now we can solve for one variable, lets use the first equation:

1bp = 22.25 - 2 ps

we can then substitute this value of bp into our second equation and solve for our ps:

2(22.25 - 2ps) + 1 ps = 37.00

44.50 - 4ps + 1 ps = 37.00
44.50 - 3 ps = 37.00
-3 ps = -7.5
ps = 2.5

plug this into equation one and

1 bp + 2(2.5) = 22.25

1 bp + 5 = 22.25

1 bp = 17.25

So 1 backpack costs $17.25 and 1 pencil set costs $2.50

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