Question

Katie's Bakery sells muffins, donuts, and cupcakes. A muffin sells for $1.05, a donut for $1.35, and cupcakes for $2.25. On a VERY busy Friday, the bakery sold 20 more muffins than cupcakes, and 30 more donuts than muffins, for a total of $200.40 for all three bakery items. How many of each baked item were sold on this busy Friday?

a) 40 muffins, 60 donuts, 20 cupcakes
b) 60 muffins, 90 donuts, 30 cupcakes
c) 50 muffins, 80 donuts, 30 cupcakes
d) 45 muffins, 75 donuts, 25 cupcakes

Answer 1

By setting up a system of equations and substituting the variables based on the given information, we deduced that Katie's Bakery sold 60 muffins, 90 donuts, and 30 cupcakes on the busy Friday.

Step-by-step explanation:

To determine how many of each baked item were sold on the busy Friday at Katie's Bakery, we need to set up a system of equations based on the given prices and totals. Let's define the following variables: M for muffins, D for donuts, and C for cupcakes.

From the problem, we have three pieces of information:

1. M = C + 20 (20 more muffins than cupcakes)
2. D = M + 30 (30 more donuts than muffins)
3. 1.05M + 1.35D + 2.25C = 200.40 (total sales)

By substitution, we can solve these equations. From the first equation, M - C = 20. From the second, we can express D in terms of M: D = M + 30. Substituting these into the third equation allows us to solve for C (cupcakes).

Now we solve:

1. Substitute M and D in the sales equation:
2. 1.05(C + 20) + 1.35(C + 20 + 30) + 2.25C = 200.40
3. Simplify and solve for C.
4. Once C is known, calculate M and D using the first two equations.

After solving, we find that the number of muffins (M), donuts (D), and cupcakes (C) sold that match the total sales amount are Option B: 60 muffins, 90 donuts, and 30 cupcakes.