Each polio vaccination consist of four doses, and each measles vaccination consist of two doses. Last year, Dr. Potter gave a total of 60 vaccinations that consisted of a total 184 doses. How many polio vaccination and how many measles vaccinations did Dr. Potter give last year?

Question

Mathematics

Christopher Roth

1 June, 18:15

Each polio vaccination consist of four doses, and each measles vaccination consist of two doses. Last year, Dr. Potter gave a total of 60 vaccinations that consisted of a total 184 doses. How many polio vaccination and how many measles vaccinations did Dr. Potter give last year?

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Answers (1)

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Bryce Coffey · Answer 1

To solve this equation we need to set up a system of equations because we need to find out the value of 2 variables given 2 equations

Equation 1: Polio vaccination has 4 doses, measles vaccination has 2 doses, and he gave out 184 doses total

Equation 2: He gave 2 types of vaccinations: polio and measles, and he gave a total of 60 vaccinations.

To convert the word form of these equations, we first have assign polio and measles a variable to make them easier to keep track of

Lets just say that the number of polio shots = x and number of measles shots = y

Equation 1: 4 doses of x added with 2 doses of y equaled 184 doses total

4x+2y = 184

Equation 2: x vaccines added with y vaccines equaled 60 total vaccines

x + y = 60

We know have our system of equations

Equation 1: 4x+2y = 184

Equation 2: x + y = 60

To solve a system of equations, we can either do elimination or substitution, depending on which is easier.

In this case, substitution is pretty easy because for equation 2 we just need to have only 1 variable on a side then we can substitute it into equation 1

Equation 2: x + y = 60

Lets subtract x from both sides of the equation to "move" the x to the other side

y = - x + 60

And using y in terms of x, we can plug it into equation 1

Equation 1: 4x+2y = 184

4x+2 (-x + 60) = 184

Now distribute the 2 to (-x+60)

4x-2x+120 = 184

Simplify by combining like terms

2x+120 = 184

Subtract 120 from both sides of the equation so all variables are on one side and the constants on the other

2x = 64

Divide 2 from both sides of the equation to isolate x, when we want to find

x = 32

Now we know the number of polio vaccines he gave, plug this into an equation to find y - the number of measles vaccine

Equation 2: x + y = 60

32 + y = 60

Subtract 32 from both sides to isolate y

y = 28

We know now that x, the number of polio vaccinations = 32 and y, the number of measles vaccinations = 28

Dr. Potter gave 32 polio vaccinations and 28 measles vaccinations last year.