A box contains some mangosteens, mangoes and passion fruits. 0.4 of the mangosteens is equal to 80% of the mangoes. The number of passion fruits is ⁵₈ of the total number of mangoes and mangosteens. If there are 84 more passion fruits than mangoes, how many fruits are there in the box altogether?

Mangosteens	Mangoes	Passion Fruits
2x8	1x8
8x3		5x3
16 u	8 u	15 u

0.4 = ⁴₁₀= ²₅
80% = ⁸⁰₁₀₀ = ⁴₅

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

2x25x2 of the mangosteens = 4x15x1 of the mangoes
410 of the mangosteens = 45 of the mangoes 

Mangosteens : Mangoes
10 : 5 _(÷5)
2 : 1

The total number of mangosteens and mangoes is repeated.  Make the total number of mangosteens and mangoes the same.  LCM of 3 and 8 is 24.

Number of more passion fruits than mangoes
= 15 u - 8 u
= 7 u

7 u = 84

1 u = 84 ÷ 7 = 12

Number of the fruits in the box altogether
= 16 u + 8 u + 15 u
= 39 u
= 39 x 12
= 468

Answer(s): 468