Solved on Nov 16, 2023

Dr. Potter gave $60$ vaccinations with a total of $184$ doses. Each polio vaccination has $4$ doses, and each measles vaccination has $2$ doses. Find the number of polio and measles vaccinations given.

STEP 1

Assumptions1. Each polio vaccination consists of4 doses. Each measles vaccination consists of doses3. Dr. Potter gave a total of60 vaccinations4. These vaccinations consisted of a total of184 doses

STEP 2

Let's denote the number of polio vaccinations as and the number of measles vaccinations as $M$. We can set up the following two equations based on the problem1. The total number of vaccinations is equal to the number of polio vaccinations plus the number of measles vaccinations. + M =60 $2. The total number of doses is equal to four times the number of polio vaccinations plus two times the number of measles vaccinations.$ 4 +2M =184$$

STEP 3

We can simplify the second equation by dividing it by2, which gives us $2 + M =92$

STEP 4

Now we have a system of two equations $+ M =60$ $2 + M =92$ We can subtract the first equation from the second to solve for 2 + M - ( + M) =92 -60$$

STEP 5

implify the equation to find the value of =92 -60 =32$$

STEP 6

Now that we have the value of , we can substitute it into the first equation to solve for $M $32 + M =60$ $

STEP 7

olve for $M$ $M =60 -32 =28$ So, Dr. Potter gave32 polio vaccinations and28 measles vaccinations last year.

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Dr. Potter gave $60$ vaccinations with a total of $184$ doses. Each polio vaccination has $4$ doses, and each measles vaccination has $2$ doses. Find the number of polio and measles vaccinations given.

STEP 1

Assumptions1. Each polio vaccination consists of4 doses. Each measles vaccination consists of doses3. Dr. Potter gave a total of60 vaccinations4. These vaccinations consisted of a total of184 doses

STEP 2

STEP 3

We can simplify the second equation by dividing it by2, which gives us $2 + M =92$

STEP 4

Now we have a system of two equations $+ M =60$ $2 + M =92$ We can subtract the first equation from the second to solve for 2 + M - ( + M) =92 -60$$

STEP 5

implify the equation to find the value of =92 -60 =32$$

STEP 6

Now that we have the value of , we can substitute it into the first equation to solve for $M $32 + M =60$ $

STEP 7

olve for $M$ $M =60 -32 =28$ So, Dr. Potter gave32 polio vaccinations and28 measles vaccinations last year.

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Dr. Potter gave 606060 vaccinations with a total of 184184184 doses. Each polio vaccination has 444 doses, and each measles vaccination has 222 doses. Find the number of polio and measles vaccinations given.

STEP 1

Assumptions1. Each polio vaccination consists of4 doses. Each measles vaccination consists of doses3. Dr. Potter gave a total of60 vaccinations4. These vaccinations consisted of a total of184 doses

STEP 2

STEP 3

We can simplify the second equation by dividing it by2, which gives us2+M=922 + M =922+M=92

STEP 4

Now we have a system of two equations+M=60 + M =60+M=602+M=922 + M =922+M=92We can subtract the first equation from the second to solve for 2 + M - ( + M) =92 -60$$

STEP 5

implify the equation to find the value of =92 -60 =32$$

STEP 6

Now that we have the value of , we can substitute it into the first equation to solve for $M32+M=6032 + M =6032+M=60$

STEP 7

olve for MMMM=60−32=28M =60 -32 =28M=60−32=28So, Dr. Potter gave32 polio vaccinations and28 measles vaccinations last year.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Dr. Potter gave $60$ vaccinations with a total of $184$ doses. Each polio vaccination has $4$ doses, and each measles vaccination has $2$ doses. Find the number of polio and measles vaccinations given.

We can simplify the second equation by dividing it by2, which gives us $2 + M =92$

Now we have a system of two equations $+ M =60$ $2 + M =92$ We can subtract the first equation from the second to solve for 2 + M - ( + M) =92 -60$$

Now that we have the value of , we can substitute it into the first equation to solve for $M $32 + M =60$ $

olve for $M$ $M =60 -32 =28$ So, Dr. Potter gave32 polio vaccinations and28 measles vaccinations last year.