SOLUTION: find two consecutive odd integers whose product is 15 more than three times their sum.
My guess is x(x+2)=3x+15, when I work this problem I have to use the quadratic formula to
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Question 115286: find two consecutive odd integers whose product is 15 more than three times their sum.
My guess is x(x+2)=3x+15, when I work this problem I have to use the quadratic formula to get an answer I don't think is correct, 1/2 +- square root of 15.
Thank you
LeeAnn
Found 3 solutions by stanbon, ganesh, MathLover1:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find two consecutive odd integers whose product is 15 more than three times their sum.
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Odd integers are always one more (or less) than even integers.
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1st odd integer: 2x+1
next odd integer:2x+3
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EQUATION:
(2x+1)(2x+3)= 3[(2x+1)+(2x+3)] + 15
4x^2 + 8x + 3 = 12x+27
4x^2 -4x -24 = 0
x^2-x-6 = 0
(x-3)(x+2) = 0
x = 3 or x=-2
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If x=3 you get:
2x+1 = 7 and 2x+3 = 9
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If x = -2 you get:
2x+1 = -3 and 2x+3 = -1
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Cheers,
Stan H.
Answer by ganesh(20) (Show Source): You can put this solution on YOUR website!
Let x and x + 2 be two consecutive odd integers.
Their product is x (x+2)= x^2 + 2x.
Their sum is x + x + 2 = 2x + 2.
Three times their sum = 3 (2x + 2) = 6x + 6.
Given that, their product is 15 more than three times their sum.
This can be mathematically written as x^2 + 2x = 6x + 6 + 15.
Simplifying, we get x^2 - 4x -21 = 0.
Solve.
x^2 - 7x + 3x - 21 = 0
Or, x(x - 7) + 3(x - 7) = 0
Or, (x - 7) (x + 3) = 0
The solutions are x = 7, -3.
So, -3, -1 is a set of solution and 7,9 is another set of solution.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
let first number be
and next number to be
their product is
their sum is
given: product is more than their sum, so we have:
write quadratic equation in standard form
.use quadratic formula to solve for
..
..
..
..
..first odd integer
solution (1)
..
..
.. first odd integer
solution (2)
Second odd integer is:
.. solution (1)
solution (2)
Check both solutions:
If
..
..
Then their product is
And their sum is ...=>...than their sum is
Difference between and is:
..
If
..
..
Then their product is
And their sum is ...=>...
than their sum is
Difference between and is:
..
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