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

He gave 32 measles vaccinations

He gave 28 polio vaccinations

Explanation:

m = measles vaccination

p = polio vaccination

m+p = 60

We know that measles is 4 doses and polio is 2 doses

4m+2p = 184

We have 2 equations and 2 unknowns

Multiply the first equation by -2

-2(m+p) = -2*60

Distribute

-2m -2p = -120

Add this to the second equation to eliminate p

4m+2p = 184

-2m -2p = -120

--------------------------

2m = 64

Divide by 2

2m/2 = 64/2

m =32

He gave 32 measles vaccinations

We still need to find the number of polio vaccinations

m+p =60

32+p = 60

Subtract 32 from each side

32-32+p = 60-32

p = 28

He gave 28 polio vaccinations