A box contains some pomegranates, apples and persimmons. 0.8 of the pomegranates is equal to 70% of the apples. The number of persimmons is ⁵₇ of the total number of apples and pomegranates. If there are 57 more persimmons than apples, how many fruits are there in the box altogether?

Pomegranates	Apples	Persimmons
7x7	8x7
7x15		5x15
49 u	56 u	75 u

0.8 = ⁸₁₀= ⁴₅
70% = ⁷⁰₁₀₀ = ⁷₁₀

0.8 of the pomegranates is equal to 70% of the apples. Make the numerators the same.  LCM of 4 and 7 is 28.

4x75x7 of the pomegranates = 7x410x4 of the apples
2835 of the pomegranates = 2840 of the apples 

Pomegranates : Apples
35 : 40 _(÷5)
7 : 8

The total number of pomegranates and apples is repeated.  Make the total number of pomegranates and apples the same.  LCM of 15 and 7 is 105.

Number of more persimmons than apples
= 75 u - 56 u
= 19 u

19 u = 57

1 u = 57 ÷ 19 = 3

Number of the fruits in the box altogether
= 49 u + 56 u + 75 u
= 180 u
= 180 x 3
= 540

Answer(s): 540