Given in the scenario:
a.) Mary made 1/5 of a batch of cookies in 1/10 of an hour.
Let's determine how many batches of cookies can she make in one hour.
Step 1: Let's convert the given into a ratio and proportion.
Mary made 1/5 of a batch of cookies in 1/10 of an hour = 1/5 : 1/10
At x = number of batches of cookies in one hour, we get = x : 1
Step 2: Let's determine the value of x.
[tex]\frac{\frac{1}{5}}{\frac{1}{10}}\text{ = }\frac{x}{1}[/tex][tex](1)(\frac{1}{5})\text{ = (x)(}\frac{1}{10})[/tex][tex]\frac{1}{5}\text{ = }\frac{1}{10}x[/tex][tex](1)(10)\text{ = (1)(5)(x) }\rightarrow\text{ 10 = 5x}[/tex][tex]\frac{5}{5}x\text{ = }\frac{10}{5}[/tex][tex]\text{ x = 2}[/tex]
Therefore, Mary can make 2 batches of cookies in one hour.