Question

Aunt Lucy is pricing cakes for a baby shower she is throwing. She wants one large cake shaped like a duckling and also some cupcakes in pastel colors. Fairview Bakery charges $3 for each cupcake, plus $25 for the large cake. Terrell's Sweet Shoppe charges $57 for the large cake and $1 for each cupcake. If Aunt Lucy orders a certain number of cupcakes, the cost will be the same at either bakery. How many cupcakes would that include? What would the total cost be?

Answer 1

After ordering 16 cupcakes the cost would be same at both the places.

The total cost at both places would $73 when 16 cupcakes are ordered.

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`

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`

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`

Combining the like terms we get;

`3x-x=57-25\\\\2x=32`

Dividing both side by 2 we get;

`(2x)/(2)=(32)/(2)\\\\x=16`

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*16=25+48 =\$73`

Total cost after 16 cupcakes at Terrell's Sweet Shoppe =
`57+x=57+16 = \$73`

Hence The total cost at both places would $73 when 16 cupcakes are ordered.