Question

Joanna went school supply shopping. She spent $27.75 on notebooks and pencils. Notebooks cost $2.30 each and pencils cost $1.25 each. She bought a total of 18 notebooks and pencils. How many of each did she buy?

A.
5 notebooks; 13 pencils
B.
3 notebooks; 15 pencils
C.
10 notebooks; 8 pencils
D.
8 notebooks; 10 pencils

Answer 1

The answer is A. 5 notebooks and 13 pencils

Explanation:

1. Identify your x and y variables.

x - number of notebooks

y - number of pencils

2. Set up two equations to come up with a system of linear equations.

x + y = 18

2.3x + 1.25y = 27.75

3. In order to solve for one of the variables (either x or y), multiply the first equation with the additive inverse (when added together, the answer is zero; one number will be positive while the other number will be negative) of the coefficient of either x or y, so you can eliminate that variable. In this case, I choose the coefficient of y which is 1.25. So, the first equation will look like this:

-1.25(x + y) = 18

-1.25x - 1.25y = -22.50

4. Next, eliminate the y variable and solve for x.

-1.25x - 1.25y = -22.50

2.3 x + 1.25 y = 27.75

__________________

1.05 x = 5.25

1.05 1.05

x = 5 Joanna bought 5 notebooks.

5. Then, solve for y.

5 + y = 18

y = 18 - 5

y = 13 Joanna bought 13 pencils.

If you want to check your work, just plug in 5 and 13 into one of the two original equations. Simplify the equations, and you should get a true statement.

5 + 13 = 18

18 = 18