A box contains some oranges, persimmons and mangosteens. 0.2 of the oranges is equal to 30% of the persimmons. The number of mangosteens is ⁵₆ of the total number of persimmons and oranges. If there are 39 less persimmons than mangosteens, how many fruits are there in the box altogether?

Oranges	Persimmons	Mangosteens
3x6	2x6
6x5		5x5
18 u	12 u	25 u

0.2 = ²₁₀= ¹₅
30% = ³⁰₁₀₀ = ³₁₀

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

1x35x3 of the oranges = 3x110x1 of the persimmons
315 of the oranges = 310 of the persimmons 

Oranges : Persimmons
15 : 10 _(÷5)
3 : 2

The total number of oranges and persimmons is repeated.  Make the total number of oranges and persimmons the same.  LCM of 5 and 6 is 30.

Number of less persimmons than mangosteens
= 25 u - 12 u
= 13 u

13 u = 39

1 u = 39 ÷ 13 = 3

Number of the fruits in the box altogether
= 18 u + 12 u + 25 u
= 55 u
= 55 x 3
= 165

Answer(s): 165