Question

James baked some cupcakes. If he gave 3 cupcakes to each cousin, he would have 25 cupcakes left. If he gave 15 cupcakes to each cousin, he would need to bake 71 more cupcakes. (a) How many cousins did he have? (b) How many cupcakes did he bake?​

Answer 1

• 8 cousins
• 49 cupcakes

Explanation:

If James gave each cousin 3 cupcakes, there would be 25 left. James is 71 cupcakes short of being able to give each cousin 15 cupcakes. You want to know the number of cousins and the number of cupcakes.

Setup

The given relations between the number of cupcakes (n) and the number of cousins (c) are ...

n -3c = 25 . . . . . 3 each ⇒ 25 left

n -15c = -71 . . . . . 15 each ⇒ 71 short

Solution

Subtracting the second equation from the first, we have ...

(n -3c) -(n -15c) = (25) -(-71)

12c = 96

c = 8 . . . . . . divide by 12

n = 3c +25 = 24 +25 = 49

(a) James has 8 cousins.

(b) James baked 49 cupcakes.