How many plain cakes did he sell that day, and how many decorated cakes did he sell that day?

Question

So a baker sells plain cakes for $7 and decorated cakes for $11. On a busy Saturday, the baker started with 120 cakes and sold and sold all but 3. His takings for the day were $992. How many plain cakes did he sell that day, and how many decorated cakes did he sell that day?

Answer 1

Start by writing expressions/equations for the information you are given.

 

A baker sells plain cakes for $7 and decorated cakes for $11.

 

Let's say;

 

p = number of plain cakes sold

d = number of decorated cakes sold

 

On a busy Saturday, the baker started with 120 cakes and sold all but 3.

 

This tells us the total number of cakes sold. (120 -3) = 117 cakes sold

 

p + d = 117  

 

His takings for the day were $992.

This tells us the money made off the 117 cakes sold. Plain are 7$ and decorated are 11$.

 

7p + 11d = 992

 

So now we have two equations we can use to solve for the two unknown variables.

 

7p + 11d = 992

p + d = 117

 

Use algebra to solve for one variable in the second equation (because it's simplest).

 

p + d  =117

p = 117 - d

 

Now substitute this in for "p" in the first equation.

 

7p + 11d = 992

7(117 - d) + 11d = 992

 

solve for d, the number of decorated cakes sold.

 

819 - 7d + 11d = 992

combine like terms

4d = 173

d = 43.25

 

Unless information is missing/incorrect in the question, it seems the baker is selling quarter pieces of cakes. Use p, the number of plain cakes sold to find d, the number of decorated cakes sold.

 

p+ d = 117

p + 43.25 = 117

p = 73.75