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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?

 Feb 20, 2021
 #1
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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.

 Feb 20, 2021

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