Question

Sarah and Joe brought homemade banana bread, cookies, and cupcakes to a fruit sale. The cookies were sold for $0.50 each, while the banana bread and cupcakes were sold for $1.75 each. They sold 40 items total and earned $52.50 total. Sarah and Joe sold twice as many cookies as banana bread. How many of each item was sold?

Define the variables for this problem.
Write a system that can be used to model the situation.
How many of each item is sold?
A. Variable a represents the number of banana bread.
B. Variable b represents the number of cookies.
C. Variable c represents the number of cupcakes.
D. 2a + b + c = 40
E. a + 0.5b + 1.75c = 52.50
F. 3a + 2b + 7c = 105
G. 3 cookies, 12 banana bread, and 25 cupcakes were sold.
H. 12 banana bread, 3 cookies, and 25 cupcakes were sold.

Answer 1

Sarah and Joe sold 5 banana bread pieces, 10 cookies, and 25 cupcakes at the fruit sale. We arrive at this by defining variables for each item sold and solving a system of equations based on the given prices and total sales.

Step-by-step explanation:

The student's question involves creating and solving a system of equations to find out how many of each item (banana bread, cookies, and cupcakes) were sold by Sarah and Joe at a fruit sale. We are told that cookies were sold for $0.50 each, while banana bread and cupcakes were sold for $1.75 each. In total, 40 items were sold for a combined total of $52.50, and there were twice as many cookies sold as banana bread.

Let's define the variables:

a = number of banana bread pieces sold

b = number of cookies sold

c = number of cupcakes sold

Now we can write a system of equations based on the given information:

1. 2a + b + c = 40 (total items sold)
2. 1.75a + 0.50b + 1.75c = 52.50 (total sales)
3. b = 2a (twice as many cookies as banana bread)

Using substitution or elimination method, we can solve this system of equations to find the values of a, b, and c. Solving gives us:

a = 5 banana bread pieces sold

b = 10 cookies sold (twice the number of banana bread)

c = 25 cupcakes sold