Standards:

CCSS.MATH.CONTENT.HSA.REI.A.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method

 

Problem:

The candy shop in town sells a bag of various candies for $40 for Halloween but it has $35 worth of candy. The rest of the $5 is for bundling, bagging, and to make some income for the store. 3 of the candies in the bag are nerds, smarties, and mints.

If x is the number of pounds of nerds, y is the number of pounds of smarties, and z is the number of pounds of mints in the bag, then I can write the following expression based on what is known about the bag of candy:

x+y+z=5

4x+6y+7z+5=40

1. How many pounds of candy are in the bag?
2. What is the price per pound of the mints?
3. What does the term 4x represent?
4. What does the expression 4x+6y+7z suppose to equal?
5. What does the whole second equation represent?

 

Commentary:

Students are asked to explain the parts of the equation without solving the actual equation. Students are evaluating the parts of the equation like the coefficient, terms, and what parts of it are being solved if there were values for x, y, and z.

 

Solutions:

1. Since x, y, and z represent the pounds of the certain types of candy in the bag, the first equation tells us that it equals 5 pounds of candy. x+y+z=5
2. The second equation is based on the price of the bag of candy. For the mints, it would be $7 per pound because it is the given coefficient for if z is the number of pounds per mints.
3. The 4x represents the value of nerds in the bag of candy. Nerds cost $4 per pound and that is multiplied by x, which is the number of pounds.
4. 4x+6y+7z would equal $35 because there is a value of $35 of candy in the bag
5. The second equation represents the total value of the bag of candy for Halloween