A student is buying pens and markers for school. Packs of pens cost $2.75 each and packs of markers cost $3.25 each. If she bought a total of 6 packs and spent $17.50, how many of each did she buy?

Answer 1

You will need to set up two equations:

A. 2.75x + 3.25y = 17.50

B. x + y = 6 (x is the number of packs of pens, and y is the number of packs of markers, and we know from the question that 6 packs total were purchased)

It is easiest to first solve for one variable in the second equation:

x + y = 6

x = 6 - y

We can then plug that into the first equation, and solve for y as normal:

2.75(6-y) + 3.25y = 17.50

16.5 - 2.75y + 3.25y = 17.50

16.5 + 0.5y = 17.50

0.5y = 1

y = 2

Now that we have a numerical value for y, we can plug that into either equation, but easiest to plug into equation 2:

x = 6 - y

x = 6 - 2

x = 4

Always check your work:

2.75x + 3.25y = 17.50

2.75(4) + 3.25(2) = 17.50

11 + 6.5 = 17.50

17.50 = 17.50

So 4 packs of pens were purchased, and 2 packs of markers were purchased.