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.

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.