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

The answer is A. 5 notebooks and 13 pencils

Step-by-step 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

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