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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 against rubella only?

Explanation	Calculations	Help
$We define variables for each group to avoid ambiguity.$	$M = number vaccinated against mumps only$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We define variables for each group to avoid ambiguity.$	$R = number vaccinated against rubella only$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We define variables for each group to avoid ambiguity.$	$B = number vaccinated against both$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "The number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps." into an equation.$	$R + B = 2(M + B)$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS1-E Click to view full details
$We translate "The number who have been vaccinated against both is twice the number who have been vaccinated against mumps." into an equation.$	$B = 2M$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS1-E Click to view full details
$We substitute B = 5000 into the second equation and solve for M .$	$M = \frac{B}{2} = \frac{5000}{2} = 2500$
$We substitute M = 2500 and B = 5000 into the first equation and solve for R .$	$R + 5000 = 2 (2500 + 5000) = 2 \times 7500 = 15000 R = 15000 - 5000 = 10000$

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10000 (Option C): 10,000 children have been vaccinated against rubella only.

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 against rubella only?

Explanation	Calculations	Help
$We define variables for each group to avoid ambiguity.$	$M = number vaccinated against mumps only$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We define variables for each group to avoid ambiguity.$	$R = number vaccinated against rubella only$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We define variables for each group to avoid ambiguity.$	$B = number vaccinated against both$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "The number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps." into an equation.$	$R + B = 2(M + B)$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS1-E Click to view full details
$We translate "The number who have been vaccinated against both is twice the number who have been vaccinated against mumps." into an equation.$	$B = 2M$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS1-E Click to view full details
$We substitute B = 5000 into the second equation and solve for M .$	$M = \frac{B}{2} = \frac{5000}{2} = 2500$
$We substitute M = 2500 and B = 5000 into the first equation and solve for R .$	$R + 5000 = 2 (2500 + 5000) = 2 \times 7500 = 15000 R = 15000 - 5000 = 10000$

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10000 (Option C): 10,000 children have been vaccinated against rubella only.