Question

Cheryl and Marcus are going to make a two-tiered cake. The smaller tier is 2/3 the size of the larger tier. The recipe for the bottom tier calls for 3/5 cup of water. How much water will they need to make the smaller tier?
They made a model to represent the problem. Cheryl says they need 6/9 cup of water. Marcus says they need 2/5 cup of water. Who is correct? Explain.

Answer 1

We are simply going to use direct proportion.

The smaller cake is 2/3 the larger cake:  let it be = (2/3)S. Let S be size of large cake

I would assume that the bottom tier refers to the larger cake.

Therefore, the bottom tier requires 3/5 cup of water.

Therefore, large cake size  S requires  (3/5) cup of water,

That means, small cake size,  (2/3)S  would require....
                                                                    = 2/3  * 3/5
                                                                     =  2/5  cup of water.
Therefore, Marcus is correct.