Natalie was saving money to buy pens. She saved $9 every 4 days. After saving for 24 days, she went to buy pens that were on sale.

1. What was the most number of pens she could buy?
2. Natalie wanted to buy 46 pens. How much more did she need to save?

(a)
Number of sets of 4 days
= 24 ÷ 4
= 6

Amount that Natalie saved in 24 days
= 6 x 9
= $54

Maximum number of sets of 7 pens that Natalie could buy 
= 54 ÷ 11
= 4 r $10

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

Maximum number of sets of 3 pens that Natalie could buy with $10
= 10 ÷ 6
= 1 r $4 

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

Maximum number of pens that Natalie could buy with $4 
= 4 ÷ 4
= 1

Most number of pens that Natalie could buy
= 4 x 7 + 1 x 3 + 1
= 28 + 3 + 1
= 32

(b)
Number of sets of 7 pens that Natalie could buy
= 46 ÷ 7
= 6 r 4

Number of sets of 3 pens that Natalie could buy
= 4 ÷ 3
= 1 r 1

Number of individual pens that Natalie could buy = 1

Amount that Natalie needed to buy 46 pens
= 6 x 11 + 1 x 6 + 4
= 66 + 6 + 4
= $76

Amount that Natalie needed to save more
= 76 - 54
= $22

Answer(s): (a) 32; (b) $22