A box contains some mangosteens, starfruits and pomegranates. 0.8 of the mangosteens is equal to 60% of the starfruits. The number of pomegranates is ⁵₈ of the total number of starfruits and mangosteens. If there are 30 less starfruits than pomegranates, how many fruits are there in the box altogether?

Mangosteens	Starfruits	Pomegranates
3x8	4x8
8x7		5x7
24 u	32 u	35 u

0.8 = ⁸₁₀= ⁴₅
60% = ⁶⁰₁₀₀ = ³₅

0.8 of the mangosteens is equal to 60% of the starfruits. Make the numerators the same.  LCM of 4 and 3 is 12.

4x35x3 of the mangosteens = 3x45x4 of the starfruits
1215 of the mangosteens = 1220 of the starfruits 

Mangosteens : Starfruits
15 : 20 _(÷5)
3 : 4

The total number of mangosteens and starfruits is repeated.  Make the total number of mangosteens and starfruits the same.  LCM of 7 and 8 is 56.

Number of less starfruits than pomegranates
= 35 u - 32 u
= 3 u

3 u = 30

1 u = 30 ÷ 3 = 10

Number of the fruits in the box altogether
= 24 u + 32 u + 35 u
= 91 u
= 91 x 10
= 910

Answer(s): 910