Question 1166462
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
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"The ratio of the length PQ to the length of QR is 3:5.
{{{x/y}}} = {{{3/5}}}
cross multiply
3y = 5x
y = {{{5/3}}}x
:
" The ratio of the length of PR to QS is 5:4.
{{{((x+y))/((y+z))}}} = {{{5/4}}}
cross multiply
5(y+z) = 4(x+y)
5y + 5z = 4x + 4y
5z = 4x + 4y - 5y
5z = 4x - y
z = {{{((4x-y))/5}}}
replace y with {{{5/3}}}x
z = {{{((4x-((5x)/3)))/5}}}
z = {{{((12x/3)-(5x/3))/5}}}
z = {{{(7x/3)*(1/5)}}}
z = {{{7x/15}}}
we can get rid of all these fractions,
 let x=15
then
y = {{{5/3}}}x
y = 25
and
z = {{{7(15)/15}}}
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