a recipe calls for 1/2 of ingredient A for every 1 2/5 cups of ingredient B. You use 2 cups of ingredient A. How many cups of ingredient B do you need?

Question

I cannot seem to understand this problem. This is also on my semester exam review homework.

Answer 1

We can solve this by making a ratio:

 

Let A = amount of ingredient A in cups

Let B = amount of ingredient B in cups

 

From the first recipe statement:

 

     (A/B) = (1/2 cup)/(1 2/5 cups)

 

     1 2/5 cups = 7/5 cups

 

     So

 

     (A/B) = (1/2)/(7/5)

 

     Cross-multiply:

 

     (7/5)A = (1/2)B

 

     Solve for B:

 

     B = 2*(7/5)A

 

     B = (14/5)A

 

 

If A = 2 cups,  then B = (14/5)* 2 cups = 28/5 cups = 5 3/5 cups

 

Answer 2

Let x = number of cups of ingredient B if 2 cups of ingredient A are used.

 

Set up a proportion:  (1/2)/(1 2/5) = (2)/x.

 

Cross multiplying we get (1/2)x = (1 2/5)(2)

 

                                    (1/2)x = 14/5, so x = 28/5 = 5 3/5 cups.