A box contains some oranges, pomegranates and persimmons. 0.4 of the oranges is equal to 20% of the pomegranates. The number of persimmons is ⁴₅ of the total number of pomegranates and oranges. If there are 18 more persimmons than pomegranates, how many fruits are there in the box altogether?

Oranges	Pomegranates	Persimmons
1x5	2x5
5x3		4x3
5 u	10 u	12 u

0.4 = ⁴₁₀= ²₅
20% = ²⁰₁₀₀ = ¹₅

0.4 of the oranges is equal to 20% of the pomegranates. Make the numerators the same.  LCM of 2 and 1 is 2.

2x15x1 of the oranges = 1x25x2 of the pomegranates
25 of the oranges = 210 of the pomegranates 

Oranges : Pomegranates
5 : 10 _(÷5)
1 : 2

The total number of oranges and pomegranates is repeated.  Make the total number of oranges and pomegranates the same.  LCM of 3 and 5 is 15.

Number of more persimmons than pomegranates
= 12 u - 10 u
= 2 u

2 u = 18

1 u = 18 ÷ 2 = 9

Number of the fruits in the box altogether
= 5 u + 10 u + 12 u
= 27 u
= 27 x 9
= 243

Answer(s): 243