a) The variables to be used are defined below.
b) A graph of an equation that models the combinations of boxes of wheat and corn cereal you can use is shown below.
c) The number of boxes of corn cereal that you need for your snack mix if you have 4 boxes of wheat cereal is 5 boxes.
d) Three other combinations of boxes of wheat and corn cereal you can use to make the same mix are (0, 8), (5, 4), and (10, 0).
In order to write a linear equation to describe this situation, we would assign variables to the number of boxes of corn cereal and wheat, and then translate the word problem into a linear equation as follows:
- Let the variable x represent the number of boxes of corn cereal.
- Let the variable y represent the number of boxes of wheat.
Part b.
Since a snack mix requires a total of 120 ounces and corn cereal are in 12 ounce boxes while wheat cereal comes in 15 ounce boxes, a linear equation that models this situation is given by;
12x + 15y = 120.
Part c.
When y is 4 boxes of wheat cereal, the value of x is given by;
12x + 15(4) = 120
12x = 120 - 60
x = 60/12
x = 5 boxes of corn cereal.
Part d.
Based on the graph of this linear equation, three other combinations of boxes of wheat and corn cereal you can use to make the same mix include;
- 0 boxes of corn cereal and 8 boxes of wheat ↔ (0, 8).
- 5 boxes of corn cereal and 4 boxes of wheat ↔ (5, 4).
- 10 boxes of corn cereal and 0 boxes of wheat ↔ (10, 0).
Complete Question;
1. A snack mix requires a total of 120 ounces of some corn cereal and some wheat cereal. Corn cereal comes in 12 ounce boxes and the wheat cereal comes in 15 ounce boxes.
a) Define the variables you will use.
b) Write and graph an equation in standard form that models that possible combinations of boxes of wheat and corn cereal you can use.
c) How many boxes of corn cereal do you need for your snack mix if you have 4 boxes of wheat cereal?
d) List 3 other combinations of boxes of wheat and corn cereal you can use to make the same mix?