Respuesta :
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:
[tex]1B = 3P[/tex]
[tex]\frac{1}{3}=\frac{P}{B}[/tex]
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:
[tex]2B = 6P[/tex]
[tex]\frac{2}{6}=\frac{P}{B}[/tex]
But [tex]\frac{2}{6}=\frac{1}{3}[/tex]
Therefore, the proportion that represents the situation remains the same [tex]1B = 3P[/tex]
This occurs because the increase in the amount of potatoes and beef was in the same proportion.