A box contains some pears, pomegranates and mangoes. 0.6 of the pears is equal to 70% of the pomegranates. The number of mangoes is ³₄ of the total number of pomegranates and pears. If there are 105 less pomegranates than mangoes, how many fruits are there in the box altogether?

Pears	Pomegranates	Mangoes
7x4	6x4
4x13		3x13
28 u	24 u	39 u

0.6 = ⁶₁₀= ³₅
70% = ⁷⁰₁₀₀ = ⁷₁₀

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

3x75x7 of the pears = 7x310x3 of the pomegranates
2135 of the pears = 2130 of the pomegranates 

Pears : Pomegranates
35 : 30 _(÷5)
7 : 6

The total number of pears and pomegranates is repeated.  Make the total number of pears and pomegranates the same.  LCM of 13 and 4 is 52.

Number of less pomegranates than mangoes
= 39 u - 24 u
= 15 u

15 u = 105

1 u = 105 ÷ 15 = 7

Number of the fruits in the box altogether
= 28 u + 24 u + 39 u
= 91 u
= 91 x 7
= 637

Answer(s): 637