A container contains some lemons, persimmons and apples. 0.6 of the lemons is equal to 70% of the persimmons. The number of apples is ⁵₇ of the total number of persimmons and lemons. If there are 46 more apples than persimmons, how many fruits are there in the container altogether?

Lemons	Persimmons	Apples
7x7	6x7
7x13		5x13
49 u	42 u	65 u

0.6 = ⁶₁₀= ³₅
70% = ⁷⁰₁₀₀ = ⁷₁₀

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

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

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

The total number of lemons and persimmons is repeated.  Make the total number of lemons and persimmons the same.  LCM of 13 and 7 is 91.

Number of more apples than persimmons
= 65 u - 42 u
= 23 u

23 u = 46

1 u = 46 ÷ 23 = 2

Number of the fruits in the container altogether
= 49 u + 42 u + 65 u
= 156 u
= 156 x 2
= 312

Answer(s): 312