Question

Youth soccer fields vary in size per the age of the players. The field for the 9 and 10 year-old players was 75 yards long by 45 yards wide. The field for the 11- 14 year old players was proportionally larger. If the length of the field for the 11-14 year old players was 100 yards, what was the width?

Answer 1

The width was 70 yards.

Answer 2

60 yards.

Explanation:

We can use the concept of proportional relationships to find the width of the field for 11-14 year-old players.

The ratio of length to width of the field for 9 and 10 year-old players is:

75 yards : 45 yards

We can simplify this ratio by dividing both sides by 15:

5 yards : 3 yards

This means that for every 5 yards in length, the field is 3 yards wide.

Now we can use this ratio to find the width of the field for 11-14 year-old players:

Ratio of length to width for 11-14 year-old players:

100 yards : w yards

where w is the unknown width.

We can set up a proportion using the ratio we found for the 9 and 10 year-old players:

5 yards : 3 yards = 100 yards : w yards

To solve for w, we can cross-multiply:

5 yards x w yards = 3 yards x 100 yards

5w = 300

w = 60

Therefore, the width of the field for 11-14 year-old players is 60 yards.