A box contains some persimmons, pomegranates and apples. 0.4 of the persimmons is equal to 80% of the pomegranates. The number of apples is ⁵₆ of the total number of pomegranates and persimmons. If there are 12 more apples than pomegranates, how many fruits are there in the box altogether?

Persimmons	Pomegranates	Apples
2x2	1x2
6x1		5x1
4 u	2 u	5 u

0.4 = ⁴₁₀= ²₅
80% = ⁸⁰₁₀₀ = ⁴₅

0.4 of the persimmons is equal to 80% of the pomegranates. Make the numerators the same.  LCM of 2 and 4 is 4.

2x25x2 of the persimmons = 4x15x1 of the pomegranates
410 of the persimmons = 45 of the pomegranates 

Persimmons : Pomegranates
10 : 5 _(÷5)
2 : 1

The total number of persimmons and pomegranates is repeated.  Make the total number of persimmons and pomegranates the same.  LCM of 3 and 6 is 6.

Number of more apples than pomegranates
= 5 u - 2 u
= 3 u

3 u = 12

1 u = 12 ÷ 3 = 4

Number of the fruits in the box altogether
= 4 u + 2 u + 5 u
= 11 u
= 11 x 4
= 44

Answer(s): 44