Find the weight

Question

A cake is cut into 3 pieces ,whose weights are in the ratio 1:2:3 . Heaviest piece is again cut and the wights are 1:2:3:4. At end of this, lightest piece is 24gms. What is the weight of original cake

Answer 1

Starting with the 4 pieces of cake, which is the second set of cuts,

 

1st piece = 24 gms

2nd piece = 48 gms

3rd piece = 72 gms

4th piece = 96 gms

 

Add up these weights to get the weight of the heaviest of the first set of cuts.

 

24 + 48 + 72 + 96 = 240

 

 

Heaviest piece of the first set of cuts is 240 gms.

 

Since the lightest piece is 1/3 the weight of the heaviest piece,

 

lightest piece = 240 / 3

lightest piece = 80 gms

 

The second heaviest piece is then double the lightest piece.

 

Second heaviest piece = 160 gms

 

 

Now that we have all of the weights of each piece, we simply add them up.

 

Original weight of cake = 80 gms + 160 gms + 240 gms

 

Original weight of cake = 480 gms

 

 

Answer 2

Hi Aarthi,

 

I hope this response will be helpful in solving this question.

 

A tip I have for you is to think about the ratio given in the question as fractions. The ratio of each piece of cake tells us how much each cake weighs relative to the smallest/ lightest piece.

 

Therefore, the heaviest piece of cake weighs 3x the weight of the lightest, and the second heaviest 2x the weight of the lightest. The sum of the weight of all three pieces equal the weight of a whole cake, which can be translated to 1x+2x+3x= weight of whole cake (x being the weight of the lightest cake).

 

This can also be visualized as the cake being cut into the sum of the numbers in the ratio, which is 6 pieces (1+2+3=6), and each slice taking the weight of however number of slices the ratio indicates.

 

1: 1/6 of the cake

2: 2/6 --> 1/3 of the cake

3: 3/6 --> 1/2 of the cake  

 

So, knowing that, the heaviest piece from the first cutting of the cake would be equivalent to 1/2 of the cake.

Now, the second part of the question can be solved using the same method.

I hope this helps in getting you started with solving the question.  Let me know if you still need help with the second half of the question, and I will be happy to help.

 

I am also available to tutor online for any other questions regarding your alebra word problems.

 

Good luck!

 

Best,

Christine