x:y=8:3 and x+y=99 work out the value of x-y
Answers
Step-by-step explanation:
Given :-
x:y = 8:3
x+y = 99
To find :-
The value of x-y
Solution :-
Given that
x:y = 8:3
It can be written as
x/y = 8/3
On applying cross multiplication then
=> 3x = 8y
=> 3x-8y = 0 --------------(1)
and given that
x+y = 99 ----------(2)
=>x = 99-y ------(3)
On substituting the value of x in (1) then
3(99-y) -8y = 0
=> 297-3y-8y = 0
=> 297-11y = 0
=> 297 = 11y
=> 11y = 297
=> y = 297/11
=> y = 27
Therefore, y = 27
On substituting the value of y in (3) then
x = 99-27
=> x = 72
Therefore, x = 72
Now,
x-y = 72-27 = 45
Therefore, x-y = 45
Answer:-
The value of x-y for the given problem is 45
Check:-
If x = 72 and y = 27 then x/y
=> 72/27
=> x/y = (8×9/(3×9)
=> x/y = 8/3
=> x:y = 8:3
and
x+y = 72+27 = 99
Therefore, x+y = 99
Verified the given relations in the given problem.
Used formulae:-
→ a:b can be written as a/b
Given :
x : y = 8 : 3
⇒ x/y = 8/3
⇒ 3x - 8y = 0 - - - - (1)
x + y = 99
⇒ x = 99 - y - - - - (2)
To Find :
value of x - y
Solution :
substitute (2) in (1), we get
⇒ 3(99 - y) - 8y = 0
⇒ 297 - 3y - 8y = 0
⇒ 11y = 297
⇒ y = 297/11
⇒ y = 27
then, substitute y = 27 in (2), we get
⇒ x = 99 - 27
⇒ x = 72
then, Finding value of x - y :
⇒ x - y
⇒ 72 - 27
⇒ 45
FINAL ANSWER :
The Value of x - y is 45 .