Question

By 7:00PM, 1/3 of the junior class had arrived at a school dance. By 8:00PM, 30 more juniors had arrived, raising the attendance to 1/2 of the junior class. How many people are in the junior class?

a. 30
b. 90
c. 120
d. 180
e. 140

Answer 1

The number of people in the junior class = 180 people

Explanation:

let number of people in junior class be x

By 7:00PM, 1/3 of the junior class had arrived at a school dance. This means x/3 juniors arrived by 7:00 PM

By 8:00PM, 30 more juniors had arrived, raising the attendance to 1/2 of the junior class. This means that 30 juniors plus 1/3 of the total number of juniors equal 1/2 of the total number of juniors

30 + x/3 = x/2

(90+x)/3 = x/2

Cross multiplying

2(90+x) = 3x

180 +2x = 3x

180 = 3x-2x

180= x

x = 180