Answer:
32 polio vaccinations and 28 measles vaccinations.
Step-by-step explanation:
Let <em>p</em> represent the number of polio vaccines and let <em>m</em> 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](https://tex.z-dn.net/?f=p%2Bm%3D60)
Together, they consisted of 184 doses.
Since each polio vaccine has 4 doses, the amount of doses for <em>p</em> polio vaccines is <em>4p</em>.
And since each measles vaccine has 2 doses, the amount of doses for <em>m</em> measles vaccines is <em>2m.</em>
So:
![4p+2m=184](https://tex.z-dn.net/?f=4p%2B2m%3D184)
We now have a system of equations:
![\left\{ \begin{array}{ll} p+m=60 &\\ 4p+2m=184 \end{array} \right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%20%20%20%20%20%20%20%20%5Cbegin%7Barray%7D%7Bll%7D%20%20%20%20%20%20%20%20%20%20%20%20p%2Bm%3D60%20%26%5C%5C%20%20%20%20%20%20%20%20%20%20%20%204p%2B2m%3D184%20%20%20%20%20%20%20%20%5Cend%7Barray%7D%20%20%20%20%5Cright.)
We can solve using elimination. Let’s multiply the first equation by -2. So:
![-2p-2m=-120](https://tex.z-dn.net/?f=-2p-2m%3D-120)
Now, we can add this to the second equation. Hence:
![(-2p+4p)+(-2m+2m)=(-120+184)](https://tex.z-dn.net/?f=%28-2p%2B4p%29%2B%28-2m%2B2m%29%3D%28-120%2B184%29)
Simplify:
![2p=64](https://tex.z-dn.net/?f=2p%3D64)
Divide both sides by 2:
![p=32](https://tex.z-dn.net/?f=p%3D32)
Therefore, Dr. Potter gave out 32 polio vaccinations.
By the first equation:
![p+m=60](https://tex.z-dn.net/?f=p%2Bm%3D60)
Substitute 32 for p to get:
![\begin{aligned} 32+m&=60 \\ m&=28\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%2032%2Bm%26%3D60%20%5C%5C%20m%26%3D28%5Cend%7Baligned%7D)
So, 28 measles vaccinations were given out.