Question

In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 5,000 have been vaccinated against both, how many have been vaccinated only against rubella?

Answer 1

10,000

Explanation:

You can start considering the number of children who have been vaccinated against both: 5000

And the number of children who have been vaccinated against both is twice the number who have been vaccinated only against mumps. This means that the number of children who have been vaccinated only against mumps is 2500 (half of 5000)

If we add the number of children who have been vaccinated against both and only mumps we get 7500. This is half the total of rubella, so rubella is 15,000 but we must substract the number of children who have been vaccinated against both so 15,000 - 5,000 = 10000

Answer 2

10,000

Explanation:

"The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps."

Let b = number of children vaccinated against both.

Let m = number of children vaccinated only against mumps.

b = 2m

"If 5,000 have been vaccinated against both"

5000 = 2m

m = 2500

5000 children are vaccinated against both.

2500 children are vaccinated only against mumps.

The total number vaccinated against mumps is the number vaccinated only against mumps plus the number vaccinated against both:

2500 + 5000 = 7500

"the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps."

total number of children vaccinated against rubella = 2 * 7500 = 15,000

5000 of those children are vaccinated against both.

15,000 - 5000 = 10,000

10,000 children are vaccinated only against rubella.

Answer: 10,000