Let's express each piece of information that we have mathematically, using the following two variables: G represents the number of crackers held per glass container and P represents the number of crackers stored in a plastic container (both maximum number stored).
"Half a dozen glass containers and 2 plastic containers can store up to 180 wheat crackers." As an equation, this sentence can be written as follows:
6G + 2P = 180
"Four glass containers can store a total of 25 more wheat crackers than 5 plastic containers."
4G = 5P + 25
"How many wheat crackers can each glass container and each plastic container store?" This question asks us for the information by which we defined our variables G and P! The two equations above are a system we can solve for G and P, which will give us the answer to this problem. Using substitution:
6G + 2P = 180
2P = 180 - 6G
P = 90 - 3G
4G = 5P + 25
4G = 5(90 - 3G) + 25
4G = 450 - 15G + 25
19G = 475
G = 25
P = 90 - 3G
P = 90 - 3(25)
P = 15
From this solution and the definitions above, we find that one glass container can store 25 crackers, and one plastic container can store 15 crackers.
