Steps
So remember that ratios are part to part, not part to whole like fractions are. In this case:
5 + 3 + 4 = 12
There are 12 parts total. This means that Pru has 5/12 of the spices, Piper has 3/12 (or 1/4) of the spices and Phoebe has 4/12 (or 1/3) of the spices. Now, we also know that Pru has 24 more spices than piper. With this info, we can set up our equation as (x = total amount of spices):
[tex]\frac{5}{12}x=\frac{3}{12}x+24[/tex]
From here we can solve for the total amount of spices. Firstly, subtract both sides by 3/12x:
[tex]\frac{2}{12}x=24[/tex]
Next, multiply both sides by 12/2 (or 6):
[tex]x=144[/tex]
There are a total of 144 spices. Now, to get Phoebe's amount of spices multiply 1/3 by 144:
[tex]\frac{144}{1}*\frac{1}{3}=\frac{144}{3}=48[/tex]
Answer:
In short, Phoebe has 48 spices.
