A box contains some persimmons, lemons and kiwis. 0.4 of the persimmons is equal to 70% of the lemons. The number of kiwis is ¹₂ of the total number of lemons and persimmons. If there are 21 more kiwis than lemons, how many fruits are there in the box altogether?

Persimmons	Lemons	Kiwis
7x2	4x2
2x11		1x11
14 u	8 u	11 u

0.4 = ⁴₁₀= ²₅
70% = ⁷⁰₁₀₀ = ⁷₁₀

0.4 of the persimmons is equal to 70% of the lemons. Make the numerators the same.  LCM of 2 and 7 is 14.

2x75x7 of the persimmons = 7x210x2 of the lemons
1435 of the persimmons = 1420 of the lemons 

Persimmons : Lemons
35 : 20 _(÷5)
7 : 4

The total number of persimmons and lemons is repeated.  Make the total number of persimmons and lemons the same.  LCM of 11 and 2 is 22.

Number of more kiwis than lemons
= 11 u - 8 u
= 3 u

3 u = 21

1 u = 21 ÷ 3 = 7

Number of the fruits in the box altogether
= 14 u + 8 u + 11 u
= 33 u
= 33 x 7
= 231

Answer(s): 231