Given:
a.) He has 12 1/2 cups of milk.
b.) The chef has 3 1/2 more cups of broth than milk.
Step 1: Since it is said that the chef has 3 1/2 more cups of broth than milk, and he has 12 1/2 cups of milk, we will be adding 3 1/2 and 12 1/2 to get the actual number of cups of broth.
We get,
[tex]\text{ 3 }\frac{1}{2}\text{ + 12}\frac{1}{2}[/tex]
In adding mixed numbers, we add separately the whole numbers and fractions and add them together later on.
[tex]\text{ 3 }\frac{1}{2}\text{ + 12}\frac{1}{2}\text{ = (Add whole numbers) + (Add fractions)}[/tex][tex]\text{ = (3 + 12) + (}\frac{1}{2}\text{ + }\frac{1}{2})[/tex][tex]\text{ = 15 + 1}[/tex][tex]\text{ = 16 cups}[/tex]
Therefore, the chef has 16 cups of broth.
Step 2: Let's now determine the remaining cups of broth after using 14 1/2 cups to make soup. We will be subtracting the current 16 cups of broth by 14 1/2 cups for the soup.
We get,
[tex]\text{ 16 - 14}\frac{1}{2}[/tex]
Let's first convert them into similar fractions before subtracting.
[tex]\text{ 16 = }\frac{16\text{ x 2}}{2}\text{ = }\frac{32}{2}[/tex][tex]\text{ 14}\frac{1}{2}\text{ = }\frac{(14\text{ x 2) + 1}}{2}\text{ = }\frac{28\text{ + 1}}{2}\text{ = }\frac{29}{2}[/tex]
Let's now proceed in subtracting them,
[tex]\text{ 16 - 14}\frac{1}{2}\text{ = }\frac{32}{2\text{ }}-\text{ }\frac{29}{2}\text{ = }\frac{\text{ 32 - 29}}{2}\text{ = }\frac{3}{2}\text{ or 1 }\frac{1}{2}\text{ cups}[/tex]
Therefore, the chef will have a remaining 1 1/2 cups of broths after using 14 1/2 cups for the soup.
