solve for x and y: 360 /x+ 300/y=14 and 300/x+360/y=13.5 please answer
Answers
Step-by-step explanation:
Given :-
360 /x+ 300/y=14
and 300/x+360/y=13.5
To find :-
Solve for x and y ?
Solution :-
Given equations are :
360 /x+ 300/y=14 ---------------(1)
=> 360(1/x)+300(1/y) = 14 ------(2)
and 300/x+360/y=13.5--------(3)
=> 300(1/x)+360(1/y) = 13.5 ----(4)
Put 1/x = a and 1/y = b then (2)&(4) becomes
=> 360a+300b = 14 ------------(5)
and
300a + 360b = 13.5 ------------(6)
On adding (5)&(6)
360a+300b = 14
300a + 360b = 13.5
(+)
_______________
660a + 660b = 27.5
________________
=> 660a + 660b = 27.5
=>660(a+b) = 27.5
=> a+b = 27.5/660
=> a+b = 275/6600
=> a+b = 11/264
=> a+b = 1/24 ---------------(7)
On subtracting (6) from (5)
360a+300b = 14
300a + 360b = 13.5
(-)
________________
60a -60b = 0.5
________________
=> 60a -60b = 0.5
=> 60(a-b) = 0.5
=> a-b = 0.5/60
=> a-b = 5/600
=> a-b = 1/120 ---------------(8)
On adding (7)&(8)
a+b = 1/24
a-b = 1/120
(+)
________________
2a+0 = (1/24)+(1/120)
________________
=> 2a = (1/24)+(1/120)
LCM of 24 and 120 = 120
=> 2a = (5+1)/120
=> 2a = 6/120
=> 2a = 1/20
=> a = 1/(20×2)
=> a = 1/40
On Substituting the value of a in (7)
=> (1/40)+b = 1/24
=> b = (1/24)-(1/40)
LCM of 24 and 40 = 120
=> b = (5-3)/120
=> b = 2/120
=> b = 1/60
Therefore, a = 1/40 and b = 1/60
a = 1/40
=> 1/x = 1/40
=> x = 40
and
b = 1/60
=> 1/y = 1/60
=> y = 60
Therefore, x = 40 and y = 60
Answer:-
The solution for the given problem is (40,60)
x= 40 and y = 60
Check:-
If x = 40 and y = 60 then
LHS of first equation 360 /x+ 300/y
=> 360/40 + 300/60
=> 9+5
=>14
=> RHS
LHS = RHS
and
LHS of equation (2) 300/x+360/y
=> 300/40+360/60
=> 30/4 + 6
=> 7.5+6
=>13.5
=> RHS
LHS = RHS is true for x= 40 and y = 60
Verified the given relations in the given problem