Find the total

Question

Savita made a large fresh cream cake . she gave 1/3 to her daughter and 1/2 to her son. Then she gave 3 pieces to her niece and 2 pieces to her nephew from the rest of the cake . fond the total number of pieces she divided the cake into and her son's and daughter's share.

Answer 1

Let x = the original number of pieces of cake

 

The total number is equal to the amount given to Savita's daughter, her son, her niece, and her nephew.

--> x = x/3 + x/2 + 3 + 2

 

Simplify and solve!

x = 2x/6 + 3x/6 + 5

x = 5x/6 + 5

6x/6 - 5x/6 = 5

x/6 = 5

x = 5(6)

x = 30

 

Be careful! The problem doesn't ask for the total number of pieces of cake! It asks for the amount given to her son and daughter. In other words, it wants the 1/3 and 1/2 amounts.

 

So what is 1/3 (x) + 1/2 (x)? Since x is 30, this is easy. 1/3 (30) = 10, and 1/2 (30) = 15, so Savita gave 25 pieces to her son and daughter. This checks, since there are five pieces remaining, and she gave five pieces to her niece and nephew.

Answer 2

The 5 pieces she gave to niece and nephew are equal to the 1/2 given to the son.

So the son got the equivalent of 5 pieces. That is a total of ten for now.

These 10 pieces were 2/3 of the cake (1/3 had gone to her daughter.)

So the cake originally had 15 pieces.

 

The daughter got 5 pieces

The son got 5 pieces.

 

Check

 

1/3 to daughter leaves 10

1/2 to her son leaves 5

5 go to niece and nephew