



 
Hi Maggie, I can show you two approaches to this problem. The first method uses some ingenuity and some arithmetic. Suppose you spend the $5.00 and buy only pencils. Pencils cost $0.50 so you would be able to purchase 10 items, all pencils. But you want 17 items so return 1 pen and get 2 pens, and now you have 9 pencils and 2 pens for a total of 11 items. The total cost is still $5.00 and thus trading a pencil for two pens leaves the cost at $5.00 but increases the number of items by 1. So start with 10 pencils. Trading a pencil for two pens increases the total number of items by 1. Thus to get to 17 items I have to trade in 7 pencils. This will leave you with 3 pencils and 14 pens. Check: 3 pencils and 14 pens is 17 items costing 3 × $0.50 + 14 × $0.25 = $1.50 + $3.50 = $5.00. The second approach is algebraic. Suppose the number of pencils you buy is x and the number of pens you buy is y. Then
and
Solve these equations for x and y. I hope this helps,  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 