Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

Aunt Nellie is pricing cakes for a baby shower she is throwing. She wants one large cake shaped like a duckling and also some cupcakes in pastel colors. Lowell Bakery charges $4 for each cupcake, plus $38 for the large cake. Gabby's Sweet Shoppe charges $60 for the large cake and $2 for each cupcake. If Aunt Nellie orders a certain number of cupcakes, the cost will be the same at either bakery. What would the total cost be? How many cupcakes would that include?

Answer 1

Let $x$ be the number of cupcakes.

Then

$$38+4\times x=60+2 \times x\\ 38+4x=60+2x$$

since the cost will be the same at either bakery.

Solving the equation we get

$$4x-2x=60-38\\ 2x=22 \implies x = 11$$

Thus, the number of cupcakes is 11.

The total cost is:

$\$ 60 + \$ 2 \times 11 = \$ 60 + \$ 2 2 =\$82\\$