Zara and Owen collect pencils and buttons. Owen has 76 less pencils than buttons. Owen has 5 times the number of pencils Zara has, and Zara has 25% more buttons than Owen. After Zara gives Owen all of her pencils and Owen gives Zara 75% of his buttons, Owen has 38 more pencils than buttons. Find the number of buttons Zara has at first.

Zara		Owen
Buttons	Pencils	Buttons	Pencils
6.25 u + 95	1 u	5 u + 76	5 u
+ 3.75 u + 57	- 1 u	- 3.75 u - 57	+ 1 u
10 u + 152	0	1.25 u + 19	6 u

100%+ 25% = 125% 

125% x 5 u
= ¹²⁵₁₀₀ x 5 u
= 6.25 u

125% x 76
= ¹²⁵₁₀₀ x 76
= 95 

75% x 5 u
= ⁷⁵₁₀₀ x 5 u
= 3.75 u  

75% x 76 
= ⁷⁵₁₀₀ x 76
= 57 

If another 38 buttons are given to Owen, he will have equal number of buttons and pencils in the end.
6 u = 1.25 u + 19 + 38
6 u - 1.25 u = 57
4.75 u = 57

1 u = 57 ÷ 4.75 = 12

Number of buttons that Zara has at first
= 6.25 u + 95
= 6.25 x 12 + 95
= 75 + 95
= 170
 
Answer(s): 170