Question

To make $ 10 $ servings of soup you need $ 4 $ cups of broth. You want to know how many servings you can make with $ 8 $ pints of broth. What proportion should you use?

Answer 1

Hint: Pint is expressed as the unit of liquid which is equal to the two cups in respect to the US (United states) standard. We will use $ 1 $ pint equal to $ 2 $ cups. Place the values in the given number of cups and will find the required value.

Complete step by step solution:
Let us assume that the number of servings per cups can be represented by $ {x_c} $ and similarly
The number of servings per pint can be represented by $ {x_p} $
Now, frame the ratio and proportion from the given word statements with respect to servings is to cups.
 $
\Rightarrow 10:4 \\
\Rightarrow {x_c}:16 \\
  $
Cross multiply the above expression –
 $ \Rightarrow 4{x_c} = 16 \times 10 $
Make the required term the subject –
 $ \Rightarrow {x_c} = \dfrac{{16 \times 10}}{4} $
Find the factors in the numerator and simplify the above expression, Common factors from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator.
 $ \Rightarrow {x_c} = 4 \times 10 = 40 $ cups ….. (A)
Similarly,
frame the ratio and proportion from the given word statements with respect to servings is to pints.
 $
  \Rightarrow 10:2 \\
\Rightarrow {x_p}:8 \\
  $
Cross multiply the above expression –
 $ \Rightarrow 2{x_p} = 10 \times 8 $
Make the required term the subject –
 $ \Rightarrow {x_p} = \dfrac{{8 \times 10}}{2} $
Find the factors in the numerator and simplify the above expression, Common factors from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator.
 $ \Rightarrow {x_p} = 4 \times 10 = 40 $ pints ….. (B)

Note: Remember the difference between words pints, cups and quarts. Quarter means the one of four equal parts into which something is divisible. Simply it is one fourth of the total. Remember the concepts and apply accordingly. You should remember the relation between the two units as it is the base of the solutions.