For the annual school food drive, 3 classes collected baskets of snack foods. Prizes were awarded to each class according to the total weight of each basket. Together, the seventh and eighth grade classes collected 145 pounds of food. The ninth and eighth grade classes collected 136 pounds of snacks. The greatest combined weight was from the seventh and ninth graders who collected 153 pounds of food. The first prize went to the class with the heaviest basket. Which class won the first, second, and third prizes? What was the total amount of snack foods collected?

This problem could be solved using a substitution equation or a diagram, like a 3-way venn diagram.

If using a linear equation with substitution, write three equations using given data.

S = seventh graders, E = eighth graders, N = ninth graders

Choose a variable and solve for it, S.

Solve for a second equation, N, so that it is stated in terms of E.

Fill in S and N in the last equation.

(145 - E) + (136 - E) = 153

145 - E + 136 - E = 153

281 - 2E = 153

- 2E = -128

-2 -2

E = 64

So, eighth graders collected 64 lbs. of snack foods. Fill this in for E in the new equations above.

S = 145 - E N = 136 - E

S = 145 - 64 N = 136 - 64

S = 81 N = 72

So, the seventh graders collected 81 pounds of snacks and the ninth grade class collected 72 lbs. of snacks.

The last question is to find the total. Add the three to find this:

S + E + N = TOTAL

81 + 64 + 72 = Total

217 pounds = Total snack foods collected