answer the following word problem by writing a system of equations to answer the word problem

Question

Joe sold a total of 10 baked goods. Each cookie costs $1.25 and each brownie cost $2.50. Joe made $20 at the bake sale. How man cookies did joe sell?

Answer 1

You will need a system of 2 equations for problems like these. We have 2 unknown values: # of cookies sold and # of brownies sold

Define your variables:

I will let c = # of cookies and let b = # of brownies

It says Joe sold 10 baked goods in total, so we know that the # of cookies and # of brownies sold combined equals 10. Therefore:

c + b = 10

Next, we know how much money was made in total ($20). We still don't know # of cookies or # of brownies, but that $20 was made by selling c cookies for $1.25 each and b brownies for $2.50 each. Therefore:

$1.25c + $2.50b = $20

c + b = 10

$1.25c + $2.50b = $20

Are the 2 equations needed to solve the word problem. Now, you can graph the 2 equations and find the point of intersection to find your solution or you can work through the system algebraically

Answer 2

x = number of cookies

y = number of brownies

10 = total number of cookies

sales for cookies = 1.25x

sales for brownies = 2.5y

20 = total sales

x + y = 10

1.25x + 2.5y = 20