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All students in Ms. Fay's Spanish class are either going on the Spain trip, the Mexico trip, or both.
1/4 of the students going to Spain are also going to Mexico,
and 2/7 of the students going on the Mexico trip are also going to Spain.
Which of the following could be the total number of students in Ms. Fay's Spanish class?
(A) 26
(B) 27
(C) 28
(D) 29
(E) 30
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Let x be the number of students going to the Spain trip;
y going to the Mexico trip;
z going to both trips.
We are given
= z,
= z.
or, equivalently,
x = 4z,
2y = 7z.
The total is x + y - z = 4z + - z = 3z + .
So we should check the appropriate values of z, if they can produce the values of the option's list.
For short, let's make a Table
T A B L E
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z 3z + (7/2)z
3 19.5
4 26
5 32.5
6 39
7 45.5
8 52
Looking in this Table, we see only ONE opportunity for possible solution: 26 students.
ANSWER. Under given conditions, the only possible solution is 26 students in the class.
Solved, with complete explanations.
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Nice problem, fresh and well posed.
My congratulations ( ! )