A box contains some apples, pomegranates and mangosteens. 0.4 of the apples is equal to 80% of the pomegranates. The number of mangosteens is ³₅ of the total number of pomegranates and apples. If there are 16 more mangosteens than pomegranates, how many fruits are there in the box altogether?

Apples	Pomegranates	Mangosteens
2x5	1x5
5x3		3x3
10 u	5 u	9 u

0.4 = ⁴₁₀= ²₅
80% = ⁸⁰₁₀₀ = ⁴₅

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

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

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

The total number of apples and pomegranates is repeated.  Make the total number of apples and pomegranates the same.  LCM of 3 and 5 is 15.

Number of more mangosteens than pomegranates
= 9 u - 5 u
= 4 u

4 u = 16

1 u = 16 ÷ 4 = 4

Number of the fruits in the box altogether
= 10 u + 5 u + 9 u
= 24 u
= 24 x 4
= 96

Answer(s): 96