SOLUTION: Albert would like to donate RM x to three relatives with nickname as P, Q and R. The ratio of money received by P, Q and R is 3 : 4 : 2. If Albert now has another new fund which

Question 1174486: Albert would like to donate RM x to three relatives with nickname as P, Q and R. The ratio of
money received by P, Q and R is 3 : 4 : 2.
If Albert now has another new fund which is four times of RM x to be contributed among
them. R receives triple amount she has from beginning, while the ratio of money received
by P and Q is 4 : 5. Write the ratio of the money they have now among P, Q and R.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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
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