the ratio of artists to spectators at the art show was 3 to 14. If a total of 1700 artists and spectators attended the art show, how many were spectators?

Answer 1

A ratio of a SUBset of people with another SUBset of people is the simplest mathematical fraction that will tell you how many of each you will have in relation to another. Therefore, by adding the two numbers of the ratio, we can determine the smallest TOTAL number of people that there could be. With a ratio of 3:14, this means our smallest total is:

3 + 14 = 17

17 people is the smallest number of people you could have that could give you a ratio of 3:14. In this problem, the total number of people was 1700. Therefore, we can divide 1700 by 17:

1700/17 = 100

We have 100 times as many of both 3 artists and 14 spectators. Therefore, we must multiply both of these numbers by 100 to get a total of 1700 and to also maintain our 3:14 ratio.

3 * 100 = 300 artists

14 * 100 = 1400 spectators

Therefore, there were 1400 spectators at the art show.

To check your answer, check the ratio between 300 and 1400 if it gives us 3:14:

300:1400 = 3:14

Also sum the two values together to see if they equal the total of 1700:

300 + 1400 = 1700

Because these two values satisfy these two conditions, we know we have the right answer.