Isaiah had 50% more buttons than Caleb. Elijah had 20% fewer buttons than Isaiah. Isaiah and Caleb gave Elijah some buttons in the ratio of 1 : 3. As a result, Elijah had 25% more buttons than before. Given that Elijah had 290 more buttons than Caleb in the end, how many buttons did Isaiah give to Elijah?

Isaiah	Caleb	Elijah
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Isaiah : Caleb = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Isaiah : Elijah = 5 : 4

The number of buttons that Isaiah had at first is repeated. Make the number of buttons that Isaiah had at first the same.  LCM of 3 and 5 is 15.

	Isaiah	Caleb	Elijah
Before	15x4 =  60 u	10x4 = 40 u	12x4 = 48 u
Change			+ 3x4 = + 12 u
Comparing the changes in the number of buttons	- 1x3 = - 3 u	- 3x3 = - 9 u	+ 4x3 = + 12 u
After	57 u	31 u	15x4 = 60 u

25% x 12 
= ²⁵₁₀₀ x 12 
= 3 

The total number of buttons that Isaiah and Caleb gave to Elijah is repeated.  Make the total number of buttons that Isaiah and Caleb gave to Elijah the same.  LCM of 4 and 3 is 12.

Number of buttons that Elijah had more than Caleb 
= 60 u - 31 u
= 29 u

29 u = 290

1 u = 290 ÷ 29 = 10

Number of buttons that Isaiah gave to Elijah
= 3 u
= 3 x 10
= 30

Answer(s): 30