A box contains some pomegranates, lemons and mangoes. 0.8 of the pomegranates is equal to 70% of the lemons. The number of mangoes is ⁵₆ of the total number of lemons and pomegranates. If there are 90 more mangoes than lemons, how many fruits are there in the box altogether?

Pomegranates	Lemons	Mangoes
7x2	8x2
6x5		5x5
14 u	16 u	25 u

0.8 = ⁸₁₀= ⁴₅
70% = ⁷⁰₁₀₀ = ⁷₁₀

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

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

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

The total number of pomegranates and lemons is repeated.  Make the total number of pomegranates and lemons the same.  LCM of 15 and 6 is 30.

Number of more mangoes than lemons
= 25 u - 16 u
= 9 u

9 u = 90

1 u = 90 ÷ 9 = 10

Number of the fruits in the box altogether
= 14 u + 16 u + 25 u
= 55 u
= 55 x 10
= 550

Answer(s): 550