Problem Solving

A college math course has 100 students enrolled, each of whom is majoring in exactly one of the following: math, physics, chemistry, biology, and engineering. Among these students, for every 5 students majoring in math, 3 are majoring in physics, and for every 5 students majoring in physics, 8 are majoring in chemistry. If 1/4 of the course students not majoring in math, physics or chemistry are majoring in biology, how many of the 100 students are majoring in engineering?

Let us assume the number of students majoring in math, physics, chemistry, biology, and engineering are m, p, c, b, and e, respectively.

So, m:p = 5:3 and p:c = 5:8 ---> m:p:c = 25:15:24
As, (m + p + c + b + e) = 100, only possible value of m, p, and c are 25, 15, and 24, respectively.

As 1/4 of the course students not majoring in math, physics or chemistry are majoring in biology, (1 - 1/4) = 3/4 of the course students not majoring in math, physics or chemistry must be majoring in engineering.

So, e = 3/4 of [100 - (m + p + c)] = 3/4 of [100 - (25 + 15 + 24)] = 3/4 of [100 - 64] = 3/4 of 36 = 27

Hello.
Could you please explain the underlined statement in the solution.

Thanks.

Atekihcan wrote:Let us assume the number of students majoring in math, physics, chemistry, biology, and engineering are m, p, c, b, and e, respectively.

So, m:p = 5:3 and p:c = 5:8 ---> m:p:c = 25:15:24
As, (m + p + c + b + e) = 100, only possible value of m, p, and c are 25, 15, and 24, respectively.

As 1/4 of the course students not majoring in math, physics or chemistry are majoring in biology, 1 - 1/4) = 3/4 of the course students not majoring in math, physics or chemistry must be majoring in engineering.

So, e = 3/4 of [100 - (m + p + c)] = 3/4 of [100 - (25 + 15 + 24)] = 3/4 of [100 - 64] = 3/4 of 36 = 27

iamniladri wrote:Could you please explain the underlined statement in the solution.

Atekihcan wrote:(1 - 1/4) = 3/4 of the course students not majoring in math, physics or chemistry must be majoring in engineering.

All the students are majoring in exactly one of the following: math, physics, chemistry, biology, and engineering. So, the students not majoring in math, physics or chemistry must be majoring in either biology or engineering.

As 1/4 of the students not majoring in math, physics or chemistry is majoring in biology, (1 - 1/4) = 3/4 of the students not majoring in math, physics or chemistry must be majoring in engineering.

Hope that helps.