### The sum of two numbers is twice their difference. If the difference of the numbers...

The sum of two numbers is twice their difference. If the difference of the numbers is P, find the larger of the two numbers
• A. p/2
• B. 3p/2
• C. 5p/2
• D. 3p
##### Explanation
Let the numbers be x and y
x+y = 2p.....(i)
x-y = p......(ii)
2x = 3p
x = 3p/2

#### Contributions (16)

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..
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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
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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..
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correct
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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
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correct.
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I got 3p/2
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correct bro
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correct..thumbs up
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Same tin for me ooooooo.... X=3p/2
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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).
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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
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• Efe timon: Thanks for d easy explanation
3 years ago
correct
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