3 friends shared a prize - solve a equation of fractions with different denominator and without specific ratio

Question

3 friends shared a prize, the 1st took 5/9 of the prize, the 2nd took 2/7 of the prize - the rest amount of the prize was equally shared to the 3 friends. If the 2nd person took $19.200, what was the amount that each of the other 2 guys took?

Answer 1

Find 5/9 + 2/7

Use 63 (9x7) as the common denominator

5/9 = 35/63 and 2/7 = 18/63, so their sum is 53/63.

The remaining prize is 63/63 - 53/63 = 10/63.

The person who won 2/7 got $19.20.

Note from above that 2/7 = 18/63 is just over 1/2 of 35/63, the first place amount, meaning the first place prize was just less than twice $19.20.

To find the first place total, multiply $19.20 by 35/18 to get $37.33

The third prize is 10/63 of the total. 10/63 is a bit more than half of 18/63.

Multiply $19.20 by 10/18 to get the third prize = $10.67.

The total prize money was $37.33 + 19.20 + 10.67 = $67.20