How many notebooks did the teacher purchase?

Question

A teacher purchased a total of 460 notebooks and pencils. Each notebook cost $1.75 in each pencil cost five cents. If the teacher spent a total of $218.50 how many notebooks did the teacher purchase?

Answer 1

For this kind of problem, you'll need to set up a system of equations.

Lets say N represents the number of notebooks the teacher bought, and P represents the number of pencils the teacher bought.

The teacher purchased a total of 460 of both of them, so we can then say that:

N + P = 460

Now if we multiply the price of each by the number purchased to get the total we can say that:

1.75N + 0.05P = 218.50

Now let's solve for 1 variable in terms of the other, lets put P in terms of N

N+P = 460

P = 460-N

... and then substitute that into the other equation

1.75N + 0.05(460-N) = 218.50 multiply out the left side to get

1.75N + 23 - 0.05N = 218.50 pull the 23 over to the right side

1.75N - 0.05N = 195.5

1.70N = 195.5

N = 115

So the teacher purchased 115 notebooks

Hope this helped!