Question

A recipe for beef stew calls for 1 pound of beef and 3 potatoes. The recipe is doubled to include 2 pounds of beef and 6 potatoes. Which propitiation represents the situation?

Answer 1

To answer the question, let B call the amount of meat and P the number of potatoes.

The recipe says that for every pound of meat we need 3 potatoes.

Then that relationship is written as follows:

$1B = 3P$

$\frac{1}{3}=\frac{P}{B}$

If we increase the amounts of the recipe by 100%, it will multiply by 2 the amount of meat and also that of potatoes. Therefore we need 2 pounds of meat and 6 potatoes.

Then the relationship is:

$2B = 6P$

$\frac{2}{6}=\frac{P}{B}$

But $\frac{2}{6}=\frac{1}{3}$

Therefore, the proportion that represents the situation remains the same $1B = 3P$

This occurs because the increase in the amount of potatoes and beef was in the same proportion.