Question

Bob uses a medium and a large measuring cup to measure the ingredients to make hisfamous Buttery Oatmeal Raisin Cookies. He wants to know how many ounces of liquideach measuring cup can hold. He first filled a 80 ounce mixing bowl with 8 large cupsand 4 medium cups of liquid. 4 large cups and 12 medium cups of liquid. How manyounces eachcupholds?

Answer 1

Note: we are assuming that Kunicki filled the 80-ounce bowl with 4 large cups and 12 medium cups of liquid.

To answer this question, we have to translate the situation into algebraic language as follows:

"He first filled an 80-ounce bowl with 8 large cups and 4 medium cups of liquid."

`8l+4m=80`

We have that the unknowns are l (the number of ounces for the large cup), and m (the number of ounces for the medium cup).

And we also have that:

He also filled the 80-ounce mixing bowl with "4 large cups and 12 medium cups of liquid", and we translate this as:

`4l+12m=80`

In this case, we end up with a linear system of equation, and we can solve this as follows:

We multiply the second equation by -2, then, we add this equation to the first equation, and then we found the value for the number of ounces of the medium cup.

To find the value of the number of ounces for the large cup, we can substitute the value of m in the first equation as follows:

`8l+4(4)=80\Rightarrow8l+16=80\Rightarrow8l=80-16\Rightarrow8l=64\Rightarrow(8l)/(8)=(64)/(8)=8`

Then, the number of ounces for the large cup is 8 ounces.

In summary, we found that the large cup holds 8 ounces, and the medium cup holds 4 ounces.