A box contains some lemons, persimmons and pomegranates. 0.4 of the lemons is equal to 30% of the persimmons. The number of pomegranates is ⁵₆ of the total number of persimmons and lemons. If there are 66 less persimmons than pomegranates, how many fruits are there in the box altogether?

Lemons	Persimmons	Pomegranates
3x6	4x6
6x7		5x7
18 u	24 u	35 u

0.4 = ⁴₁₀= ²₅
30% = ³⁰₁₀₀ = ³₁₀

0.4 of the lemons is equal to 30% of the persimmons. Make the numerators the same.  LCM of 2 and 3 is 6.

2x35x3 of the lemons = 3x210x2 of the persimmons
615 of the lemons = 620 of the persimmons 

Lemons : Persimmons
15 : 20 _(÷5)
3 : 4

The total number of lemons and persimmons is repeated.  Make the total number of lemons and persimmons the same.  LCM of 7 and 6 is 42.

Number of less persimmons than pomegranates
= 35 u - 24 u
= 11 u

11 u = 66

1 u = 66 ÷ 11 = 6

Number of the fruits in the box altogether
= 18 u + 24 u + 35 u
= 77 u
= 77 x 6
= 462

Answer(s): 462