Question

There are 100 students in a band. Ninety percent of the students are either 12 or

13 years old. The number of 13-year-olds is 125% of the number of 12-year-olds. The rest of
the students are 14 years old. Write the portion of the band for each age as a fraction and a
percent.

12-year olds: fraction: *blank*, percent: *blank*
13-year olds: fraction: *blank*, percent: *blank*
14-year olds: fraction: *blank*, percent: *blank*

Answer 1

Explanation:

Let's first find the number of 12-year-olds and 13-year-olds in the band:

Let x be the number of 12-year-olds.

Then the number of 13-year-olds is 1.25x (125% of x).

The total number of students in the band is 100, so we know that x + 1.25x = 0.9(100).

Solving for x, we get x = 40, so there are 40 12-year-olds and 50 (1.25x) 13-year-olds.

The number of 14-year-olds is the remainder after we count the 12 and 13-year-olds:

The total number of students in the band is 100, and we know that 90% of them are 12 or 13 years old, so 10% are 14 years old.

10% of 100 is 10, so there are 10 14-year-olds.

Now we can find the portion of the band for each age group:

12-year olds: fraction = 40/100 = 2/5, percent = 40%

13-year olds: fraction = 50/100 = 1/2, percent = 50%

14-year olds: fraction = 10/100 = 1/10, percent = 10%