A container contains some pears, persimmons and mangosteens. 0.4 of the pears is equal to 80% of the persimmons. The number of mangosteens is ⁵₆ of the total number of persimmons and pears. If there are 30 more mangosteens than persimmons, how many fruits are there in the container altogether?

Pears	Persimmons	Mangosteens
2x2	1x2
6x1		5x1
4 u	2 u	5 u

0.4 = ⁴₁₀= ²₅
80% = ⁸⁰₁₀₀ = ⁴₅

0.4 of the pears is equal to 80% of the persimmons. Make the numerators the same.  LCM of 2 and 4 is 4.

2x25x2 of the pears = 4x15x1 of the persimmons
410 of the pears = 45 of the persimmons 

Pears : Persimmons
10 : 5 _(÷5)
2 : 1

The total number of pears and persimmons is repeated.  Make the total number of pears and persimmons the same.  LCM of 3 and 6 is 6.

Number of more mangosteens than persimmons
= 5 u - 2 u
= 3 u

3 u = 30

1 u = 30 ÷ 3 = 10

Number of the fruits in the container altogether
= 4 u + 2 u + 5 u
= 11 u
= 11 x 10
= 110

Answer(s): 110