# Math Help - Integer Problem

1. ## Integer Problem

Five times the smallest of three consecutive odd integers is ten more than twice the largest. Find the integers.

EDIT: Mind you, I just need help with setting it up. I can solve it, I'm just having a tough time writing it down properly.

Five times the smallest of three consecutive odd integers
is ten more than twice the largest. Find the integers.

Consecutive odd integers "go up by 2's".

Let . $\begin{array}{ccc}x &=& \text{1st number} \\ x+2 &=& \text{2nd number} \\ x+4 &=& \text{3rd number}\end{array}$

$\underbrace{\text{Five times smallest}}\;\;\underbrace{\text{is}}\;\;\underbrac e{\text{twice largest}}\;\underbrace{\text{plus 10}}$

. . . . $5 \times x \qquad\qquad =\qquad2(x+4)\qquad + 10$

And there is your equation: . $5x \;=\;2(x+4) + 10$

3. Thanks, I see how it's done now.

EDIT: Wait...shouldn't there be an x+2 in there somewhere?

Thanks, I see how it's done now.

EDIT: Wait...shouldn't there be an x+2 in there somewhere?
Hello,

Nope, because they're only asking you things about the smallest and the largest of the three integers :-)

5. Ah, I see. Thanks.

6. ## hmm

Uh, doesnt 5x = 2x + 18 give x = 6

werent the integers supposed to be odd?

Five times the smallest of three consecutive odd integers is ten more than twice the largest. Find the integers.

EDIT: Mind you, I just need help with setting it up. I can solve it, I'm just having a tough time writing it down properly.
Originally Posted by Twig
Uh, doesnt 5x = 2x + 18 give x = 6

werent the integers supposed to be odd?
You are correct. (Good spot! )

So let's redo this with the smallest number being 2x + 1 and the largest being 2x + 5:
$5(2x + 1) = 2(2x + 5) + 10$

$10x + 5 = 4x + 10 + 10$

$6x = 15$

As there is no integer solution for x the problem does not have a solution. (In fact you can figure this out just by doing an "even-odd" argument: 5 times an odd number is odd; 2 times an odd number plus 10 is even. So the two sides can't be equal.)

-Dan

8. ## hey

hi dan

Yeah smart thinking with the odd times odd..

Odd*odd = odd

Odd*even = even

9. Originally Posted by Twig
hi dan

Yeah smart thinking with the odd times odd..

Odd*odd = odd

Odd*even = even
You thought there was something "odd" about it?