Kate had 96 more buttons than Violet. After Kate gave away 1/3 of her buttons and Violet gave away 3/4 of her buttons, Violet had 199 less buttons than Kate. How many buttons did Kate have at first?

Answer 1

Let the no. of buttons Violet had = x
So the no. of buttons Kate had = x + 96
By the given Question
2/3x (x + 96) - 1/4x = 199
2/3x + 64 - 1/4x = 199
2/3x - 1/4x : 199
(8x - 3x)/12 = 199
5x : 199 * 12
x : 199 * 2.4
x = 477.6
x = 478
So the no. of buttons Kate had = 96 + x
= 96 + 478
= 574