Question

Henrietta bought 5 cupcakes and 2 brownies for $16.25. She went back to the bakery the next day and bought 7 cupcakes and 6 brownies for $26.75. How much does one brownie cost? One cupcake?

Answer 1

cost of one cupcake = $2.75

cost of one brownie = $1.25

Explanation:

Let c = number of cupcakes

Let b = number of brownies

Equation 1: 5c + 2b = 16.25

Equation 2: 7c + 6b = 26.75

Multiply equation 1 by 3:

⇒ 15c + 6b = 48.75

Now subtract equation 2 from this equation to eliminate 6b:

⇒ 8c = 22

Divide both sides by 8:

⇒ c = 2.75

Substitute c = 2.75 into one of the original equations and solve for b:

⇒ 5(2.75) + 2b = 16.25

⇒ 13.75 + 2b = 16.25

⇒ 2b = 2.5

⇒ b = 1.25

Therefore, cost of one cupcake = $2.75 and cost of one brownie = $1.25