I decide to hold a little bake sale one weekend where I will be selling jumbo cupcakes at 3.50 each and cookies at 1.25 each. I have a total of 250 in both cupcakes and cookies. At the end of my bake sale I have sold all the cupcakes and cookies I baked and made a total of 506.00. How many total cupcakes did I have and how many cookies?
Let x be the number of cupcakes and y be the number of cookies sold. We can write a system of equations:
total of 250 cupcakes and cookies ==> x + y = 250 . (1)
total cost was $506 ==> 3.5x + 1.25y = 506 . (2)
We can multiply equation (1) by 5 and equation (2) by -4:
5x + 5y = 1250
-14x - 5y = -2024
Adding, we get -9x = -774, so x = 86 and y = 164.
You baked 86 cupcakes and 164 cookies.