Question

Your class sold cupcakes and brownies at a bake sale.you sold cupcakes for $1.50and brownies got $1.25.after selling 23items, you made $31.75.how many cupcakes did you sell?how many brownies?

Answer 1

12 cupcakes were sold

11 brownies were sold

Explanation:

Let c = number of cupcakes sold

Let b = number of brownies sold

Total number of items sold = 23

⇒ b + c = 23

cupcake = $1.50 each

brownie = $1.25 each

Total money made = $31.75

⇒ 1.5c + 1.25b = 31.75

Rewrite b + c = 23 to make b the subject, substitute into 1.5c + 1.25b = 31.75 and solve for c:

⇒ b = 23 - c

⇒ 1.5c + 1.25(23 - c) = 31.75

⇒ 1.5c + 28.75 - 1.25c = 31.75

⇒ 0.25c + 28.75 = 31.75

⇒ 0.25c = 3

⇒ c = 12

So 12 cupcakes were sold

Substitute found value for c into b + c = 23 and solve for b:

⇒ b + 12 = 23

⇒ b = 11

So 11 brownies were sold