Question

a half dozen cupcakes cost $15. what constant of proportionality relates the number of cupcakes and total cost? write an equation of that represents this relationship. explain and show the work in an 7th grader's work

Answer 1

Step 1 — Define variables
- Let n = number of cupcakes.
- Let C = total cost (in dollars).

Step 2 — Find the constant of proportionality
A half dozen = 6 cupcakes, and those cost $15. The constant of proportionality k is the cost per cupcake:
k = total cost ÷ number of cupcakes = 15 ÷ 6 = 15/6 = 5/2 = 2.5.

So k = 2.5 dollars per cupcake (or $2.50 per cupcake).

Step 3 — Write the equation
Cost is proportional to number of cupcakes, so
C = k · n,
plug in k = 2.5:
C = 2.5n.

Check: For 6 cupcakes, C = 2.5 × 6 = $15, which matches.

Answer: constant of proportionality = 2.5 (dollars per cupcake), equation C = 2.5n.