SOLUTION: Hi The points P Q R S lie on a straight line. The ratio of the length PQ to the length of QR is 3:5. The ratio of the length of PR to QS is 5:4. What is the ratio of the length of

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Question 1166462: Hi
The points P Q R S lie on a straight line. The ratio of the length PQ to the length of QR is 3:5. The ratio of the length of PR to QS is 5:4. What is the ratio of the length of QR to the length RS to the length of PS.
thanks
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The points P Q R S lie on a straight line.
The ratio of the length PQ to the length of QR is 3:5.
The ratio of the length of PR to QS is 5:4.
What is the ratio of the length of QR to the length RS to the length of PS.
:
:
P------x-------Q------y--------R-------z-------S
:
"The ratio of the length PQ to the length of QR is 3:5.
x%2Fy = 3%2F5
cross multiply
3y = 5x
y = 5%2F3x
:
" The ratio of the length of PR to QS is 5:4.
%28%28x%2By%29%29%2F%28%28y%2Bz%29%29 = 5%2F4
cross multiply
5(y+z) = 4(x+y)
5y + 5z = 4x + 4y
5z = 4x + 4y - 5y
5z = 4x - y
z = %28%284x-y%29%29%2F5
replace y with 5%2F3x
z = %28%284x-%28%285x%29%2F3%29%29%29%2F5
z = %28%2812x%2F3%29-%285x%2F3%29%29%2F5
z = %287x%2F3%29%2A%281%2F5%29
z = 7x%2F15
we can get rid of all these fractions,
let x=15
then
y = 5%2F3x
y = 25
and
z = 7%2815%29%2F15
z = 7
:
So we have
x: PQ=15
Y: QR=25
z: RS=7
therefore
PS = 15+25+7 = 47
:
What is the ratio of the length of QR to the length RS to the length of PS.
25:7:47

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Technically, the statement of the problem is faulty. There are different solutions possible for different orderings of the four points.

For solving the problem, I will assume the four points are in the given order.

P.....Q.....R.....S

(1) The ratio of PQ:QR is 3:5. So let PQ=3x and QR=5x:

P<-- 3x -->Q<-- 5x -->R.....S

(2) The ratio of PR:QS is 5:4. Currently PR is 8x. Change the scale so that PR is a multiple of 5:

P<-- 15x -->Q<-- 25x -->R.....S

Now PR is 40x; the ratio 5:4 means QS is 32x. Since QR is 25x, RS is 7x:

P<-- 15x -->Q<-- 25x -->R<-- 7x -->S

Now you can answer the question. QR is 25x; RS is 7x; PS is 47x. So

QR:RS:PS = 25:7:47