Question 1174486
p to q to r = 3 to 4 to 2 when the total distributed is equal to x.

if x = 9, then:

p = 3
q = 4
r = 2


when x = 9, 4x = 36 and r is tripled to equal 6.


the ratio of r to the total is 6/36 = 1/6 * the total.


this means that p + q = 5/6 * the total.


since p / q = 4 / 5, then solve for p to get p = 4/5 * q


since p + q = 5/6 * the total, replace p with 4/5 * q to get:


4/5 * q + q = 5/6 * the total.


combine like terms to get 9/5 * q = 5/6 * the total.


solve for q to get q = 5/9 * 5/6 * the total = 20/54 * the total.


since p/q = 4/5, solve for q to get q = 5/4 * p


since p + q = 5/6 * the total, replace q with 5/4 * p to get:


p + 5/4 * p = 5/6 * the total.


combine like terms to get 9/4 * p = 5/6 * the total.


solve for p to get p = 4/9 * 5/6 * the total = 20/54 * the total.


r = 1/6 * the total * 9/9 = 9/54 * the total.


you get:


p = 20/54 * the total
q = 25/54 * the total
r = 9/54 * the total


the ratio of p to q to r becomes 20 to 25 to 9.


to test if this is correct, do the following:


let x = 27
p = 3/9 * 27 = 9
q = 4/9 * 27 = 12
r = 2/9 * 27 = 6


then 4x = 4 * 27 = 108
p = 20/54 * 108 = 40
q = 25/54 * 108 = 50
r = 9/54 * 108 = 18


r is equal to 6 when x = 27
r is equal to 18 when 4x = 108


when the total is 108, r becomes 3 times what it was when the total was 27.
this can also be shown as:
when the total is 4x, r becomes 3 times what it was when the total was x.


i'll go with:


if the total is x, then the ratio of p to q to r is 3 to 4 to 2.
if the total is 4x, then the ratio of p to q to r is 20 to 25 to 9


it's a little messy, but i think it's right.


let me know if this is the answer they are looking for.


theo