Howard had some pens. He gave ³₄ of his pens to Warren and bought 4 new pens. After that, he gave ⁴₉ of his remaining pens to his brother and bought another 7 new pens. In the end, Howard had 27 pens.

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

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

⁵₉ of his remaining pens = 27 - 7 = 20
¹₉ of his remaining pens = 20 ÷ 5 = 4
⁴₉ of his remaining pens = 4 x 4 = 16

Number of pens that Howard gave to his brother = 16

(b)
⁹₉ of his remaining pens = 9 x 4 = 36

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

¹₄ of his total pens = 36 - 4 = 32
⁴₄ of his total pens = 4 x 32 = 128

Number of pens that Howard had at first = 128 

Answer(s): (a) 16; (b) 128