2 numbers are first added together and then multiplied together. The numbers added together = 18 and the numbers multiplied together = 45. What are the 2 numbers?
Question asked by: knowitall
Comment or provide your answer to this question
The two numbers are 15 & 3... Doesn't matter which order you choose to put them in, it'll still work.
Here's how I came up with it using algebra:
Firstly note:
a x b = 45
therefore: b = 45/a (equation 1)
Second, note that:
a + b = 18 (equation 2)
now we can substitute equation 2 into equation 1:
a + (45/a) = 18
rearraning:
a - 18 + (45/a) = 0
multiply by factor of a:
a^2 - 18a + 45 = 0 (equation 3)
Thirdly, note that equation 3 is a solveable quadratic equation with real solutions of a=3 and a=15.
Substituting either solution back into equation 1 gives:
a=3 and b=15
or
a=15 and b=3
QED.
By: Sacha001
Date of comment: Thu, Jul 15th 2010
Yeah, I think the person asking the question wants to see the algebraic arithmatic actually working out the answer!
By: sb70520
Date of comment: Sun, Jun 13th 2010
First no is 15 and secon no is 3
when you will add 15+3=18
when you will multiply 15*3=45
By: susanta
Date of comment: Wed, Jul 22nd 2009
Comments and other answers:
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The two numbers are 15 & 3... Doesn't matter which order you choose to put them in, it'll still work.
Here's how I came up with it using algebra:
Firstly note:
a x b = 45
therefore: b = 45/a (equation 1)
Second, note that:
a + b = 18 (equation 2)
now we can substitute equation 2 into equation 1:
a + (45/a) = 18
rearraning:
a - 18 + (45/a) = 0
multiply by factor of a:
a^2 - 18a + 45 = 0 (equation 3)
Thirdly, note that equation 3 is a solveable quadratic equation with real solutions of a=3 and a=15.
Substituting either solution back into equation 1 gives:
a=3 and b=15
or
a=15 and b=3
QED.
By: Sacha001
Date of comment: Thu, Jul 15th 2010
Profile Picture
Yeah, I think the person asking the question wants to see the algebraic arithmatic actually working out the answer!By: sb70520
Date of comment: Sun, Jun 13th 2010
Profile Picture
First no is 15 and secon no is 3
when you will add 15+3=18
when you will multiply 15*3=45By: susanta
Date of comment: Wed, Jul 22nd 2009
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