lan583 wrote:
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?
A. 2,500
B. 7,500
C. 10,000
D. 15,000
E. 17,500
We can create the following formula:
Total = total mumps + total rubella - both + neither
We can let total mumps = m, and thus total rubella = 2m.
We can let both = b, and thus only mumps is m - b.
Since the number who have been vaccinated against both is twice the number who have been vaccinated only against mumps:
b = 2(m - b)
b = 2m - 2b
3b = 2m
Since b = 5000, we have:
3(5000) = 2m
15000 = 2m
7500 = m
Since m = 7500, the total number of children vaccinated against rubella is r = 2m = 2(7500) = 15000. Thus, the number who have been vaccinated against only rubella is r - b = 15000 - 5000 = 10000.
Answer: C
_________________