Please help with this Ratio question

Question

Pritam, Sarah and Emily share some money in the ratios 3:6:4 Sarah gets $15 more than Emily. Work out the amount of money that Pritam gets?

Answer 1

Hints:

$6x=\$15+4x$.

What is $x$?

What is $3x$?

Answer 2

Hint:

Let $x$ be the amount of money Emily gets. Then Sarah gets $x + 15$. Then, it is trivial to calculate $x$ with the help of the given ratios. $$\dfrac{x}{4} = \dfrac{x + 15}{6}$$ Finally, let $y$ be the amount of money Pritam gets. Now that we know $x$, we can use the given ratios to calculate $y$. $$\dfrac{x}{4} = \dfrac{y}{3}$$

Answer 3

Apologies for the formatting here.

Let

P = Pritam's money

S = Sarah's

E = Emily's

We know:

(1) S = E + 15

(2) S/E = 6/4

Multiplying both sides of (2) by E, we have:

S = 1.5E

Substituting this for S in (1), we get:

1.5E = E + 15

0.5E = 15

E = 30

From the original ratio we have:

P/E = 3/4

P = 0.75E

P = 0.75 * 30 = 22.5