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.
