The sum of two numbers is twice their difference. If the difference of the numbers is P, find the larger of the two numbers
p/2
3p/2
5p/2
3p
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x+y=2p..(1) x-y=p..(2)
from eqn 1.. y=2p-x substitute 'y' into eqn 2 x-2p+x=p.. therefore x=3p/2
substitute value of x into eqn 1..so;
3p/2+y=2p therefore y=p/2
(x=3p/2 and y=p/2)..x is the greater number..
X + Y = 2t ........... equation1
X - Y = t ........... equation2
add equation 1$2 since X is the biggest number
2X = 3t
divide both side by 2
X = 3t/2
let the number be a and b
therefore
a+b=2p.......(1)
a-b=, p......(2)
(eliminate , get the value of b)
2b=p
b=p/2
(subtitute b=p/2 in equation 2)
a-p/2=p
(find the LCM of dinominator and multiply althrough)
2a-p=2p
collect like term
2a=3p
divide althrough by the coeficient of a
a=3p/2
therefore 3p/2 is the larger number
x+y =2p
x- y = p
From eq 1 .. y= 2p - x
Eq 2.... x - (2p - x) = p
x = p + 2p - x
x + x = 3p
2x = 3p
x = 3p/2
x+y=2p..(1) x-y=p..(2)
from eqn 1.. y=2p-x substitute ''y'' into eqn 2 x-2p+x=p.. therefore x=3p/2
substitute value of x into eqn 1..so;
3p/2+y=2p therefore y=p/2
(x=3p/2 and y=p/2)..x is the greater number..
X y =2p.....(equ.1)
x- y = p ..........(equ.2)
making y the subject from equ.1
y =2p-x.
Substituting y into (lets say) eq.2
x-2p-x =p
2x = 3p
x = 3p/2
to find y....substitute the value of x into equation(1)
3p/2 y = 2p
y = 2p-3p/2
4p-3p/2
p/2.
So therefore, y=p/2 and x= 3p/2(which is the biggest).
Let the numbers be x and y.
From the first statement: x y=2(x-y)
where x-y= p.......................(1)
Therefore x y=2p ............ (2)
equation 1 divide 2
2x=3p
x=3p/2 ans
