Which Carrots Should You Buy?

 
You are at the grocery store and have a coupon for $0.50 off of two 16 oz. bags of carrots.  You notice that the 16 oz. bags of carrots are selling for $1.99 each and the 32 oz. bags of carrots are selling for $2.99 each.
 

• Which carrots should you buy if you want to get the most carrots for your money?

 

These questions may be useful in helping students down the problem solving path:

• What information would be useful in figuring this out?
• What assumptions are we making?

 

There are several ways students may attempt to solve this problem.  Assuming they don’t go the “Ew, I hate carrots and wouldn’t buy either!” route, then most likely they will either:

• figure out how much 32 oz. (2 lb) cost for both sizes and see that the two 16 oz. bags of carrots will cost $3.48 before taxes versus the $2.99 for the 32. oz bag.
• find the unit price as a $/oz and compare that.

 

• The coupon

• The 16 oz (1 lb) bag of carrots that you can use the coupon on

• The 32 oz (2 lb) bag of carrots

• CCSS 6.RP.1 – Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
• CCSS 6.RP.2 – Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
• CCSS 6.RP.3 – Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

 

• Grocery store