How many polio vaccinations and how many measles vaccinations did Dr. Potter give last year?

Question

Dr. Potter provides vaccinations against polio and measles. Each polio vaccination consists of 4 doses, and each measles vaccination consists of 2 doses. Last year, Dr. Potter gave a total of 60 vaccinations that consisted of a total of 184 doses. How many polio vaccinations and how many measles vaccinations did Dr. Potter give last year?

Answer 1

Let's establish that x= number of polio vaccinations and y=number of measles vaccinations.

Since Dr. P gave a total of 60 VACCINATIONS, we know that x+y=60. (This is equation #1)

We also know that Dr. P gave a total of 184 DOSES of the vaccinations and that the polio vaccine has 4 doses, while the measles vaccine has 2 doses. This means that our second equation is 4x+2y=184. (This is equation #2)

You can get either variable (x or y) by itself from equation #1. I always choose x.

x+y=60

-y. -y

x=60-y

Now we can plug our x value into equation #2.

4x+2y=184

4(60-y)+2y=184

240-4y+2y=184

240-2y=184

-240 -240

-2y=-56

/-2 /-2

y=28 measles vaccines

So we know that Dr. P administered 28 measles vaccines. We need to plug our y value back into equation #1 (or, to make it easier, our switched around equation) to find the number of polio vaccines.

x=60-y

x=60-28

x=32 polio vaccines