Japheth had some pens. He gave ²₃ of his pens to Julian and bought 4 new pens. After that, he gave ²₇ of his remaining pens to his sister and bought another 7 new pens. In the end, Japheth had 47 pens.

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

(a)
Fraction of  his remaining pens after he gave to his sister
= 1 - ²₇
= ⁵₇

⁵₇ of his remaining pens = 47 - 7 = 40
¹₇ of his remaining pens = 40 ÷ 5 = 8
²₇ of his remaining pens = 2 x 8 = 16

Number of pens that Japheth gave to his sister = 16

(b)
⁷₇ of his remaining pens = 7 x 8 = 56

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

¹₃ of his total pens = 56 - 4 = 52
³₃ of his total pens = 3 x 52 = 156

Number of pens that Japheth had at first = 156 

Answer(s): (a) 16; (b) 156