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

Let \( p \) be the number of polio vaccinations and \( m \) be the number of measles vaccinations. We can set up the following equations based on the information given:

1. The total number of vaccinations given is:
\[
p + m = 60
\]

2. The total number of doses is:
\[
4p + 2m = 184
\]

Now we have a system of equations to solve.

First, we can simplify the second equation by dividing everything by 2:
\[
2p + m = 92
\]

Now we have the following system:
\[
\begin{align*}
1. & \quad p + m = 60 \\
2. & \quad 2p + m = 92
\end{align*}
\]

Next, we can solve for \( m \) in terms of \( p \) using the first equation:
\[
m = 60 - p
\]

Now, substitute \( m \) into the second equation:
\[
2p + (60 - p) = 92
\]

Combine like terms:
\[
2p - p + 60 = 92
\]
\[
p + 60 = 92
\]

Subtract 60 from both sides:
\[
p = 32
\]

Now that we have \( p \), we can find \( m \):
\[
m = 60 - p = 60 - 32 = 28
\]

Thus, Dr. Potter gave:
- \( p = 32 \) polio vaccinations,
- \( m = 28 \) measles vaccinations.

In conclusion, Dr. Potter gave \( 32 \) polio vaccinations and \( 28 \) measles vaccinations.