'manpreet singh wrote:If 3/7 of the students in a room are seniors and 7/25 of the remaining students are juniors, and there are x students in the room who are neither juniors nor seniors, how many students are in the room?
Although manpreet hasn't included the necessary answer choices, I think this is a question type known as "Variables in the Answer Choices," where each answer choice is a variable expression written in terms of x.
Let's solve it.
Let T = Total number of students in room
So, T = (
# of seniors) + (
# of juniors) + (
others)
3/7 of the students in a room are seniors
So, the
# of seniors = (3/7)T
IMPORTANT: We've already accounted for 3/7 of the students. So, 4/7 of the students are not yet accounted for. So, the number of remaining (unaccounted for) students =
(4/7)T
7/25 of the remaining students are juniors
So,
# of juniors = (7/25)
(4/7)T
=
(4/25)T
There are x students in the room who are neither juniors nor seniors
So,
# of others = x
We're now ready . . .
T = (
# of seniors) + (
# of juniors) + (
others)
T =
(3/7)T +
(4/25)T +
x
Get common denominator: T =
(75/175)T +
(28/175)T +
x
Simplify: T = (103/175)T + x
Subtract (103/175)T from both sides to get: (72/175)T = x
Multiply both sides by (175/72) to get: T = [spoiler](175/72)x[/spoiler]
Aside: If the question were worded, "
Which of the following is a possible value of x?," we'd need to recognize that x must be divisible by 72.
Cheers,
Brent
