1. In 25 minutes Li can run 10 laps around the track. Determine the number of laps she can run per minute. a. Find the constant of proportionality in this situation.
b. Write an equation to represent the relationship.

2. Jennifer is shopping with her mother. They pay $2 per pound for tomatoes at the vegetable stand.
a. Find the constant of proportionality in this situation.
b. Write an equation to represent the relationship.
3. On average, Susan downloads songs per month. An online music vendor sells package prices for songs that can be downloaded onto personal digital devices. The graph below shows the package prices for the most popular promotions. Susan wants to know if she should buy her music from this company or pay a flat fee of per month offered by another company. Which is the better buy?

a. Find the constant of proportionality for this situation.
b. Write an equation to represent the relationship.

c. Use your equation to find the answer to Susan’s question above. Justify your answer with mathematical evidence and a written explanation.

For the first example, the constant of proportionality should be .4 of a mile, meaning that Li can run .4 mile per minute. The equation should be .4x = y. For the second example, it is easy to find the constant of proportionality because it is given, which is 2. The equation to represent this would be 2x = y.

Step-by-step explanation:

The reason why the constant of proportionality is .4 is because I used the ratio from before and compared it to the one needed. I simply turned the ratios into fractions and I cross multiplied before turning it into a equation to solve to find .4 as the constant of proportionality. The equation should be .4x = y because x = the amount of minutes Li ran, and y = the total amount of miles she ran. The reason why the constant of proportionality is 2 in the second problem is because Jennifer is paying 2 per pound, which is the unit rate. If we are looking at the cost per pound, it would mean that 2 is the constant of proportionality. The reason why the equation to represent this would be 2x = y is because x = the amount of pounds, and y = the total amount of money, which represents the situation.