Joanna went school supply shopping.

Question

The rest of the question:

She spent $26.79 on notebooks and pencils. Notebooks cost $2.43 each and pencils cost $1.11 each. She bought a total of 17 notebooks and pencils. How many of each did she buy?

Answer 1

This is a system of equations question. To construct the equations you need, you ought to find the different types of objects involved and clarify them with different variables. Let's call notebooks x and pencils y.

x = the number of notebooks

y = the number of pencils

So the total number of objects is 17.

That means x+y=17

You can multiply the number of notebooks or pencils bought by the sale price to see how much they cost individually, which means you can write

2.43x = notebooks cost

1.11y = pencils cost

The pencils cost + the notebooks cost = the total cost

Therefore 2.43x + 1.11y = 26.79 because they give you 26.79 as the total cost.

With these two equations we can find x and y through substitution or elimination, which you are probably covering around this time. I will cover the substitution method.

With substitution you put one of the variables in terms of the other. So for this problem we can change

x + y = 17

into

x = 17 - y

by subtracting y from both sides.

Then we plug in this substituted equation into our other one,

2.43x + 1.11y = 26.79

2.43(17 - y) + 1.11y = 26.79

distribute

41.31 - 2.43y + 1.11y = 26.79

subtract 41.31 and combine ys

-1.32y = -14.52

y = 11 pencils

then plug y into one of the equations, in this case

x + y = 17 is easier

x + 11 = 17

subtract 11 from both sides

x = 6 notebooks

Therefore she bought 6 notebooks and 11 pencils.