Gwen was saving money to buy pens. She saved $4 every 8 days. After saving for 64 days, she went to buy pens that were on sale.

1. What was the most number of pens she could buy?
2. Gwen wanted to buy 33 pens. How much more did she need to save?

(a)
Number of sets of 8 days
= 64 ÷ 8
= 8

Amount that Gwen saved in 64 days
= 8 x 4
= $32

Maximum number of sets of 7 pens that Gwen could buy 
= 32 ÷ 11
= 2 r $10

Remaining amount left after buying sets of 7 pens = $10

Maximum number of sets of 4 pens that Gwen could buy with $10
= 10 ÷ 7
= 1 r $3 

Remaining amount left after buying sets of 4 pens = $3

Maximum number of pens that Gwen could buy with $3 
= 3 ÷ 3
= 1

Most number of pens that Gwen could buy
= 2 x 7 + 1 x 4 + 1
= 14 + 4 + 1
= 19

(b)
Number of sets of 7 pens that Gwen could buy
= 33 ÷ 7
= 4 r 5

Number of sets of 4 pens that Gwen could buy
= 5 ÷ 4
= 1 r 1

Number of individual pens that Gwen could buy = 1

Amount that Gwen needed to buy 33 pens
= 4 x 11 + 1 x 7 + 3
= 44 + 7 + 3
= $54

Amount that Gwen needed to save more
= 54 - 32
= $22

Answer(s): (a) 19; (b) $22