A box contains some persimmons, mangosteens and apples. 0.6 of the persimmons is equal to 70% of the mangosteens. The number of apples is ²₃ of the total number of mangosteens and persimmons. If there are 32 more apples than mangosteens, how many fruits are there in the box altogether?

Persimmons	Mangosteens	Apples
7x3	6x3
3x13		2x13
21 u	18 u	26 u

0.6 = ⁶₁₀= ³₅
70% = ⁷⁰₁₀₀ = ⁷₁₀

0.6 of the persimmons is equal to 70% of the mangosteens. Make the numerators the same.  LCM of 3 and 7 is 21.

3x75x7 of the persimmons = 7x310x3 of the mangosteens
2135 of the persimmons = 2130 of the mangosteens 

Persimmons : Mangosteens
35 : 30 _(÷5)
7 : 6

The total number of persimmons and mangosteens is repeated.  Make the total number of persimmons and mangosteens the same.  LCM of 13 and 3 is 39.

Number of more apples than mangosteens
= 26 u - 18 u
= 8 u

8 u = 32

1 u = 32 ÷ 8 = 4

Number of the fruits in the box altogether
= 21 u + 18 u + 26 u
= 65 u
= 65 x 4
= 260

Answer(s): 260