Question

plz help Pru, Piper, and Phoebe share spices in the ratio 5:3:4. If Pru has 24 more spices than Piper, how many spices does Phoebe have?

Answer 1

48 spices

Explanation:

The number of spices each has is a multiple of 5, 3, and 4.

The number of spices each has is 5x, 3x, and 4x.

Pru has 5x spices.

Piper has 3x spices.

Pru has 24 more spices than Piper, so

5x = 3x + 24

2x = 24

x = 12

Phoebe has 4x spices, so Phoebe has

4(12) = 48

Answer 2

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):

`(5)/(12)x=(3)/(12)x+24`

From here we can solve for the total amount of spices. Firstly, subtract both sides by 3/12x:

`(2)/(12)x=24`

Next, multiply both sides by 12/2 (or 6):

`x=144`

There are a total of 144 spices. Now, to get Phoebe's amount of spices multiply 1/3 by 144:

`(144)/(1)*(1)/(3)=(144)/(3)=48`

Answer:

In short, Phoebe has 48 spices.