Question

There are 24 people running in a race. 1/4 are wearing green shorts. 1/6 are wearing red shorts. The rest are wearing blue shorts. How many people are wearing blue shorts?

Use a tape diagram to help you answer the question.
Solve. Show or explain your work.

Answer 1

To use a tape diagram, we can start by drawing a rectangle to represent the total number of people in the race. Then, we can divide it into four equal parts to represent the people wearing green shorts and into six equal parts to represent the people wearing red shorts.

Let's use the letter "B" to represent the number of people wearing blue shorts. We know that the total number of people is 24, so we can write:

4 parts + 6 parts + B parts = 24

Simplifying this equation, we get:

10 + B = 24

Subtracting 10 from both sides, we get:

B = 14

Therefore, 14 people are wearing blue shorts.

To double-check our answer, we can add up the number of people in each category:

4 parts out of 24 = 6 people wearing green shorts

6 parts out of 24 = 4 people wearing red shorts

B parts out of 24 = 14 people wearing blue shorts

6 + 4 + 14 = 24, which matches the total number of people in the race.

Answer 2

First, let's find the fraction of people wearing green or red shorts:

1/4 + 1/6 = 3/12 + 2/12 = 5/12

This means that 5/12 of the people are wearing either green or red shorts. To find the fraction of people wearing blue shorts, we need to subtract this from 1 (since the three options are exhaustive):

1 - 5/12 = 7/12

So, 7/12 of the people are wearing blue shorts. To find out how many people this represents, we can multiply this fraction by the total number of people in the race:

7/12 x 24 = 14

Therefore, 14 people are wearing blue shorts.

Explanation: