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?
Dr. Potter gave
polio vaccinations and
measles vaccinations.

Answer 1

polio= 32 measel= 28

Explanation:

Answer 2

32 polio vaccinations and 28 measles vaccinations.

Explanation:

Let p represent the number of polio vaccines and let m represent the amount of measles vaccines.

We know that each polio vaccine consists of 4 doses, and each measles vaccine consists of 2 doses.

Dr. Potter gave a total of 60 vaccinations last year. Therefore, the sum of the number of polio vaccines and measles vaccines must total 60. Therefore:

`p+m=60`

Together, they consisted of 184 doses.

Since each polio vaccine has 4 doses, the amount of doses for p polio vaccines is 4p.

And since each measles vaccine has 2 doses, the amount of doses for m measles vaccines is 2m.

So:

`4p+2m=184`

We now have a system of equations:

`\left\{ \begin{array}{ll} p+m=60 &\\ 4p+2m=184 \end{array} \right.`

We can solve using elimination. Let’s multiply the first equation by -2. So:

`-2p-2m=-120`

Now, we can add this to the second equation. Hence:

`(-2p+4p)+(-2m+2m)=(-120+184)`

Simplify:

`2p=64`

Divide both sides by 2:

`p=32`

Therefore, Dr. Potter gave out 32 polio vaccinations.

By the first equation:

`p+m=60`

Substitute 32 for p to get:

`\begin{aligned} 32+m&=60 \\ m&=28\end{aligned}`

So, 28 measles vaccinations were given out.