Question 1174127: All 210 students in a school went roller skating, to a water park, or both. The number of students who went only to the water park is four times the number of students who went only roller skating. The number of students who went only to the water park is two times the number of students who did both. How many students did both?
Answer by ikleyn(52803)   (Show Source):
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All 210 students in a school went roller skating, to a water park, or both. The number of students who went only to the water park
is four times the number of students who went only roller skating. The number of students who went only to the water park is two times
the number of students who did both. How many students did both?
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water park only BOTH roller skating only
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4y = 2x x y
Let x = "How many students did both". and let y = "roller skating only" (see the Figure above)
From the Figure and from the condition, we have these equations
x + y + 2x = 210 (1)
4y = 2x (2)
We simplify equation (2) to x = 2y, and substitute this expression into equation (1).
We have then
(2y) + y + 2*(2y) = 210
2y + y + 4y = 210
7y = 210
y = 210/7 = 30.
Thus x = 30: 30 students did BOTH. ANSWER
Solved.
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