Avery had 40% more pens than Layla. Aria had 20% fewer pens than Avery. Avery and Layla gave Aria some pens in the ratio of 3 : 4. As a result, Aria had 50% more pens than before. Given that Aria had 250 more pens than Layla in the end, how many pens did Avery give to Aria?

Avery	Layla	Aria
7x5	5x5
5x7		4x7
35	25	28

100% + 40% = 140%
140% = ¹⁴⁰₁₀₀ = ⁷₅

Avery : Layla = 7 : 5

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Avery : Aria = 5 : 4

The number of pens that Avery had at first is repeated. Make the number of pens that Avery had at first the same.  LCM of 7 and 5 is 35.

	Avery	Layla	Aria
Before	35x1 =  35 u	25x1 = 25 u	28x1 = 28 u
Change			+ 14x1 = + 14 u
Comparing the changes in the number of pens	- 3x2 = - 6 u	- 4x2 = - 8 u	+ 7x2 = + 14 u
After	29 u	17 u	42x1 = 42 u

50% x 28 
= ⁵⁰₁₀₀ x 28 
= 14 

The total number of pens that Avery and Layla gave to Aria is repeated.  Make the total number of pens that Avery and Layla gave to Aria the same.  LCM of 7 and 14 is 14.

Number of pens that Aria had more than Layla 
= 42 u - 17 u
= 25 u

25 u = 250

1 u = 250 ÷ 25 = 10

Number of pens that Avery gave to Aria
= 6 u
= 6 x 10
= 60

Answer(s): 60