Question

Two customers go to a bakery to buy cupcakes and muffins. Each cupcake costs the same amount and each muffin costs the same amount.

• The first customer paid $18.56 for 4 cupcakes and 2 muffins.
• The second customer paid $19.78 for 2 cupcakes and 4 muffins.

What is the cost in dollars of each cupcake?
A. $3.50
B. $2.89
C. $2.00
D. $4.00

Answer 1

To find the cost of each cupcake, we set up a system of equations using the given information. We can solve the system of equations to find the values of x and y, and ultimately determine the cost of each cupcake. The cost of each cupcake is $2.00.

Step-by-step explanation:

To find the cost of each cupcake, we need to set up a system of equations based on the information given. Let's assign the unknown cost of a cupcake as x and the unknown cost of a muffin as y.

From the first customer, we know that 4x + 2y = 18.56. From the second customer, we know that 2x + 4y = 19.78.

We can solve this system of equations using the method of substitution or elimination to find the values of x and y. Once we have these values, we will know the cost of each cupcake.

Let's solve the equations using the method of elimination:

• 1. Multiply the first equation by 2 and the second equation by 4 to make the coefficients of x in both equations equal.
• 2. Subtract the second equation from the first equation to eliminate x.
• 3. Solve the resulting equation to find the value of y.
• 4. Substitute the value of y into either of the original equations to solve for x.
• 5. The value of x will be the cost of each cupcake.

After solving the equations, we find that x = 2.00. Therefore, the cost of each cupcake is $2.00.