Application algebra problem

Question

At the store, you buy some pencils for $0.50 each and some pens for $1.50 each. You spend a total of $12 and purchase 16 items (pencils and pens only). (a) Write and solve a system of equations that model the problem. Show all your work. (b) How many of each type of writing utensil did you purchase?

Answer 1

In order to solve this one you want to start by setting up a system of equations using the information … so if you use p to represent the number of pencils and n to represent the number of pens, that would be

p + n = 16

0.5p + 1.5n = 12

to solve then you want to plug in p = 16 – n into the second expression

0.5(16 – n) + 1.5n = 12

8 – 0.5n + 1.5n = 12

n = 4

then go back to the first equation to solve for the value of p

p + 4 = 16

p = 12

meaning that the scenario works if you bought 12 pencils and 4 pens