Question

A bakery posts a sale on Groupon to purchase 16 cupcakes for $20. Maxx, finds that the unit rate is 125 and writes the equations 1.25. What does 1.25 represent in his equation? • Luca finds that the unit rate is 0.8 and writes the equation = 0.81r. What does 0.8 represent in his equation? Both equations are mathematically correct depending on how the variables are defined. Why does Maxx's equation make more sense than Luca's equation based on the given scenario?

Answer 1

First, the number 1.25 represents the constant ratio of change of the problem, that is, the unit rate or price per cupcake, mainly because is the coefficient of x.

Second, Luca's unit rate is not correct because each cupcake costs $1.25, not $0.80. This happened because Luca divided 16/20 which doesn't make sense. So, 0.80 doesn't mean anything to the problem as it's being defined.

However, if we call y the number of cupcakes and x the price, then 0.80 would be the ratio of change in that case.

Third, Max equation make more sense because the independent variable (x) should represent the number of cupcakes, and the dependent variable (y) should represents the cost because the total cost will always depend on the number of cupcakes.