Answer:
32 polio vaccinations and 28 measles vaccinations.
Step-by-step 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:
[tex]p+m=60[/tex]
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:
[tex]4p+2m=184[/tex]
We now have a system of equations:
[tex]\left\{ \begin{array}{ll} p+m=60 &\\ 4p+2m=184 \end{array} \right.[/tex]
We can solve using elimination. Let’s multiply the first equation by -2. So:
[tex]-2p-2m=-120[/tex]
Now, we can add this to the second equation. Hence:
[tex](-2p+4p)+(-2m+2m)=(-120+184)[/tex]
Simplify:
[tex]2p=64[/tex]
Divide both sides by 2:
[tex]p=32[/tex]
Therefore, Dr. Potter gave out 32 polio vaccinations.
By the first equation:
[tex]p+m=60[/tex]
Substitute 32 for p to get:
[tex]\begin{aligned} 32+m&=60 \\ m&=28\end{aligned}[/tex]
So, 28 measles vaccinations were given out.
