Warren had some pens. He gave ²₃ of his pens to Reggie and bought 4 new pens. After that, he gave ²₅ of his remaining pens to his sister and bought another 7 new pens. In the end, Warren had 40 pens.

1. How many pens did Warren give to his sister?
2. How many pens did Warren have at first?

(a)
Fraction of  his remaining pens after he gave to his sister
= 1 - ²₅
= ³₅

³₅ of his remaining pens = 40 - 7 = 33
¹₅ of his remaining pens = 33 ÷ 3 = 11
²₅ of his remaining pens = 2 x 11 = 22

Number of pens that Warren gave to his sister = 22

(b)
⁵₅ of his remaining pens = 5 x 11 = 55

Fraction of his total pens after he gave to Reggie
= 1 - ²₃
= ¹₃

¹₃ of his total pens = 55 - 4 = 51
³₃ of his total pens = 3 x 51 = 153

Number of pens that Warren had at first = 153 

Answer(s): (a) 22; (b) 153