Question

Each of the performers at a circus convention is either a unicyclist, a mime or an aerial artist. The ratio of unicyclists to mimes is 3: 14 The ratio of unicyclists to aerial artists is 9 : 11 There are 88 aerial artists. What percentage of the performers are unicyclists? Give your answer to 2 d.p.​

Answer 1

14.52%

Explanation:

U/A = 9/11 and A = 88 multiply by 8/8 ( to get A=88 as given)

9/11 * 8/8 = 72/88 = U / A so U = 72

Then U/M = 3/14 multiply by 24/24 ( to get U = 72 as found above)

then U/M= 72 / 336 M = 336

U / ( A + U + M ) x 100% = 14.52 %

Answer 2

14.52% are unicyclists

Explanation:

First, we can use proportions to find the number of unicyclists at the convention. Since we know that the ratio of unicyclists to aerial artists is 9:11, and there are 88 aerial artists, we can set up the following equation:

`(9)/(11)=(x)/(88)`

If we cross multiply, we get that 11x = (88)(9). After we divide through by 11 to isolate x, we get that x = (8)(9) = 72

Second, we have to figure out the number of mimes at the convention to figure out the total number of people there. We know that the ratio of unicyclists to mimes is 3:14, and the number of unicyclists is 72. So, we can set up the following proportion:

`(3)/(14)=(72)/(y)`

If we cross multiply, we get that 3y = 1008, or y = 336 mimes

The total number of people at the convention is 336 mimes + 72 unicyclists + 88 unicyclists = 496. Now we have to figure out what percent of 496 is 72 (the number of unicyclists). If we let z = the percentage, we can simply set up an equation that says that 72 is z% of 496:

`72=0.01z*496\\0.01z=0.14516\\z=14.52`

This means that approximately 14.52% of the performers are unicyclists.