Answer:
After ordering 16 cupcakes the cost would be same at both the places.
The total cost at both places would <u>$73</u> when 16 cupcakes are ordered.
Step-by-step explanation:
We need to find the number of cup cakes Aunt Lucy ordered when the cost will be the same at either bakery.
Also What will be the Total cost.
Given:
Fairview Bakery charges:
Cost of each cup cake = $3
Cost of large cake = $25
Let the number of cupcakes ordered be 'x'.
So we can say that;
Total cost will be equal to sum of Cost of large cake and Cost of each cup cake multiplied by number of cupcakes ordered.
framing in equation form we get;
Total cost = ![25+3x](https://tex.z-dn.net/?f=25%2B3x)
Terrell's Sweet Shoppe charges:
Cost of each cup cake = $1
Cost of large cake = $57
So we can say that;
Total cost will be equal to sum of Cost of large cake and Cost of each cup cake multiplied by number of cupcakes ordered.
framing in equation form we get;
Total cost = ![57+x](https://tex.z-dn.net/?f=57%2Bx)
To find the number of cupcakes ordered for the total cost would be same at both place we will make both the equations equal.
So we get;
![25+3x=57+x](https://tex.z-dn.net/?f=25%2B3x%3D57%2Bx)
Combining the like terms we get;
![3x-x=57-25\\\\2x=32](https://tex.z-dn.net/?f=3x-x%3D57-25%5C%5C%5C%5C2x%3D32)
Dividing both side by 2 we get;
![\frac{2x}{2}=\frac{32}{2}\\\\x=16](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B2%7D%3D%5Cfrac%7B32%7D%7B2%7D%5C%5C%5C%5Cx%3D16)
Hence After ordering 16 cupcakes the cost would be same at both the places.
Total cost after 16 cupcakes at Fairview Bakery =
![25+3x=25+3\times16=25+48 =\$73](https://tex.z-dn.net/?f=25%2B3x%3D25%2B3%5Ctimes16%3D25%2B48%20%3D%5C%2473)
Total cost after 16 cupcakes at Terrell's Sweet Shoppe = ![57+x=57+16 = \$73](https://tex.z-dn.net/?f=57%2Bx%3D57%2B16%20%3D%20%5C%2473)
Hence The total cost at both places would <u>$73</u> when 16 cupcakes are ordered.