1. A cupcake show makes and delivers specialized cupcakes. It will cost someone $30 for 10 cupcakes and $67.50 for 25 cupcakes. This total includes the cost per cupcake and
delivery fee. How much does each cupcake cost? (enter your answer with just the number,
no $ sign)

2.5

Explanation:

The given costs for the purchase and delivery of the cupcakes are;

The cost of 10 cupcakes and the delivery fee = $30

The cost of 25 cupcakes and the delivery fee = $67.50

Let 'c' represent the fixed cost of delivery of the cup cakes, and let 'x' represent the cost of each cup cake, we have;

30 = 10·x + c...(1)

67.50 = 25·x + c...(2)

Subtracting equation (1) from equation (2) gives;

67.50 - 30 = 37.50 = 25·x - 10·x + c - c = 15·x

∴ x = 37.50/15 = 2.5

The cost of each cupcake, x = 2.5

(∴ The delivery fee = 30 - 10 × 2.5 = 5)

The cost of each cupcake is 2.5.