Howard had some buttons. He gave ³₄ of his buttons to Warren and bought 4 new buttons. After that, he gave ⁵₉ of his remaining buttons to his brother and bought another 7 new buttons. In the end, Howard had 31 buttons.

1. How many buttons did Howard give to his brother?
2. How many buttons did Howard have at first?

(a)
Fraction of  his remaining buttons after he gave to his brother
= 1 - ⁵₉
= ⁴₉

⁴₉ of his remaining buttons = 31 - 7 = 24
¹₉ of his remaining buttons = 24 ÷ 4 = 6
⁵₉ of his remaining buttons = 5 x 6 = 30

Number of buttons that Howard gave to his brother = 30

(b)
⁹₉ of his remaining buttons = 9 x 6 = 54

Fraction of his total buttons after he gave to Warren
= 1 - ³₄
= ¹₄

¹₄ of his total buttons = 54 - 4 = 50
⁴₄ of his total buttons = 4 x 50 = 200

Number of buttons that Howard had at first = 200 

Answer(s): (a) 30; (b) 200