Question

Laura is baking a cake. The recipe says that she has to mix 64 grams of chocolate powder into the flour. Laura knows that 1 cup of that particular chocolate powder has a mass of 128 grams. She added two over three of a cup of chocolate powder to the flour. Should Laura add more chocolate powder to make the exact recipe, or did she go over and by what amount?

She went over by one over three of a cup.
She needs to add one over three of a cup.
She needs to add one over six of a cup.
She went over by one over six of a cup.

Answer 1

Option 4 - She went over by one over six of a cup.

Explanation:

Given : Laura is baking a cake. The recipe says that she has to mix 64 grams of chocolate powder into the flour.

Laura knows that 1 cup of that particular chocolate powder has a mass of 128 grams. She added two over three of a cup of chocolate powder to the flour.

To find : Should Laura add more chocolate powder to make the exact recipe, or did she go over and by what amount?

Solution :

The required mass of chocolate powder in two over three of a cup of chocolate powder with mass 128 grams.

Multiply 128 by two over three

`128* (2)/(3) =85.33\ gm`

`85.33\ gm >64\ gm`

So, Laura added more chocolate powder to make the exact recipe

Now, The amount of chocolate Laura added too much to make the exact recipe

Subtract 64 grams from 85.33 grams

`85.33-64=21.33 gm`

The amount she needs to add.

Now, 64 grams represent

`(64)/(128)=((64)/(64))/((128)/(64))=(1)/(2)` of a cup of chocolate

She added 2/3 of a cup of chocolate powder to the flour.

If we compare:

`(2)/(3) =0.67 > (1)/(2) =0.5`

Then, she went over by:

`(2)/(3) -(1)/(2) =((2(2)-3(1))/(6)=(4-3)/(6)=(1)/(6)`

Therefore, Option 4 is correct.

She went over by one over six of a cup.