A container contains some persimmons, passion fruits and mangosteens. 0.2 of the persimmons is equal to 30% of the passion fruits. The number of mangosteens is ⁵₈ of the total number of passion fruits and persimmons. If there are 108 less passion fruits than mangosteens, how many fruits are there in the container altogether?

Persimmons	Passion Fruits	Mangosteens
3x8	2x8
8x5		5x5
24 u	16 u	25 u

0.2 = ²₁₀= ¹₅
30% = ³⁰₁₀₀ = ³₁₀

0.2 of the persimmons is equal to 30% of the passion fruits. Make the numerators the same.  LCM of 1 and 3 is 3.

1x35x3 of the persimmons = 3x110x1 of the passion fruits
315 of the persimmons = 310 of the passion fruits 

Persimmons : Passion Fruits
15 : 10 _(÷5)
3 : 2

The total number of persimmons and passion fruits is repeated.  Make the total number of persimmons and passion fruits the same.  LCM of 5 and 8 is 40.

Number of less passion fruits than mangosteens
= 25 u - 16 u
= 9 u

9 u = 108

1 u = 108 ÷ 9 = 12

Number of the fruits in the container altogether
= 24 u + 16 u + 25 u
= 65 u
= 65 x 12
= 780

Answer(s): 780