A box contains some pomegranates, mangosteens and pears. 0.6 of the pomegranates is equal to 80% of the mangosteens. The number of pears is ⁵₆ of the total number of mangosteens and pomegranates. If there are 204 less mangosteens than pears, how many fruits are there in the box altogether?

Pomegranates	Mangosteens	Pears
4x6	3x6
6x7		5x7
24 u	18 u	35 u

0.6 = ⁶₁₀= ³₅
80% = ⁸⁰₁₀₀ = ⁴₅

0.6 of the pomegranates is equal to 80% of the mangosteens. Make the numerators the same.  LCM of 3 and 4 is 12.

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

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

The total number of pomegranates and mangosteens is repeated.  Make the total number of pomegranates and mangosteens the same.  LCM of 7 and 6 is 42.

Number of less mangosteens than pears
= 35 u - 18 u
= 17 u

17 u = 204

1 u = 204 ÷ 17 = 12

Number of the fruits in the box altogether
= 24 u + 18 u + 35 u
= 77 u
= 77 x 12
= 924

Answer(s): 924