Student Question

Of 450 students assembled for a concert, 40 percent were boys. After a bus containing an equal number of boys and girls brought more students to the concert, 41 percent of the students at the concert were boys. What is the number of students on the bus?

Expert Answers

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Before the bus drops the students at the concert assembly hall, there are 450 students in the hall waiting for the concert to begin. Of these 450 students, we are told that 40% were boys. This means that 180 of the 450 students were boys (180 divided by 450 equals 40%). This also means that the remaining 270 students waiting in the concert hall are girls, as girls comprise 60% of the total number of students assembled.

In order to make the numbers work so the number of boys assembled for the concert equals 41% of the total, there have to be 48 students on the bus. Of these 48 students, an equal number are girls and boys. In other words, there are 24 girls on the bus and 24 boys. The number of girls and boys assembled both increase by the above noted additional students. Thus, once the bus drops the students at the concert hall, there are 498 students in the assembly hall waiting for the concert (the original 450 plus the 48 additional students).

Since there were an equal number of girls and boys on the bus, this means that of the 498 students waiting for the concert to begin, 294 are girls (270 plus 24 equals 294) and 204 are boys (180 plus 24 equals 204).

As a result of the new students, 41% of the students now are boys (204 divided by 498 equals 41%) and 59% are girls (294 divided by 498).

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