3/4 of a whole cake was eat on on Sunday. If two pieces are eaten Monday and three pieces are left, how many pieces of cake were there to start?

Question

3/4 of a whole cake was eaten on Sundat.  If two pieces are eaten Monday and three pieces are left, how many pieces of cake were there to start?

Answer 1

There are four quarters in one whole pie.⊕  shade out three of these quarters as they were eaten on Sunday. One quarter is left. Next, split that quarter into 5 equal parts as two pieces were eaten on Monday and there are still 3 pieces that are still left (2+3=5 total pieces in each quarter of the pie). Last, multiply 5 pieces, 4 times, as there are four quarters per whole pie. The total number of pieces is 20. 

The total number of pieces that have already been eaten is

17/20 + (the uneaten pieces 3/20)=20/20

Answer 2

If 3/4 of the cake is already eaten by Sunday, then everything eaten after that is 1/4. A total of 5 pieces are eaten after Sunday, therefore 5 is 1/4 of the whole cake. So to solve, you would use the equation 5= 1/4x. Multiply each side by 4 to find x (the whole amount of the cake). If the equations aren't clear, draw a picture to help you see the fractions. There were 20 pieces to start with.

Answer 3

Let x = the number of pieces of cake that you started with.

 

3/4th of the cake being eaten, means that 1/4 of the cake is left = (1/4)x

 

Therefore, since 2 additional pieces were eaten on monday, a total of (1/4)x - 2 pieces are left.

 

If only three were left, this implies the equation:

 

(1/4)x - 2 = 3

 

Solving:

 

(1/4)x = 5

x=20