# Translating a Word Problem into an Algebraic Equation

Find two consecutive odd integers such that three times the smaller one exceeds two times the larger one by $7$.

• What have you attempted so far? – daOnlyBG Nov 7 '14 at 18:45
• Unfortunately nothing :( – mohmmed Nov 7 '14 at 18:49
• by my Guess the answer is 11,13 but i don't how i make it in formulas – mohmmed Nov 7 '14 at 18:51
• no body can solve it?! – mohmmed Nov 7 '14 at 18:59
• I answered a similar quesiton a little while ago, you might try to read that answer to get some more practice for turning words into algebraic expressions. – Eric Stucky Nov 7 '14 at 22:25

Let $x$ be the least of two consecutive odd numbers. So the greater of the two consecutive odd numbers must be $x+2$.

Now, we want [three times the smaller odd number] to exceed [twice the larger odd number] by $7$. So the difference between $3x$ and $2(x+1)$ should equal seven.

$$3x -2(x+2) = 7 \quad\iff \quad x = 11$$

So we have the least of the odd numbers. What is the next consecutive odd number after $x$?

• thenk you for explien :) – mohmmed Nov 7 '14 at 19:59
• by mean = here? – mohmmed Nov 7 '14 at 20:00

"Find two consecutive odd integers..."

OK, that's $2k+1, \space2k+3$, where $k\in \mathbb{Z}$.

"...such that three times the smaller one..."

$$3(2k+1)$$

"...exceeds two times the larger one..."

$$2(2k+3)$$

..."by 7."

$$3(2k+1)=2(2k+3)+7$$

Solve for $k=5$, and then plug that into $2k+1$ and $2k+3$ to get $11$ and $13$, respectively.

• why you put 2k ?? – mohmmed Nov 7 '14 at 19:44
• i don't get it , – mohmmed Nov 7 '14 at 19:48
• What is an even number? – daOnlyBG Nov 7 '14 at 19:50
• I know what the Question mean, but what have to do with that? – mohmmed Nov 7 '14 at 19:52
• If you answer me, I can explain to you how I got 2k+1. – daOnlyBG Nov 7 '14 at 19:52

Three times the smaller one exceeds two times the larger one by 7.

$\text{Three times the smaller one} = \text{(two times the larger one)} + 7$.

$3\times\text{the smaller one} = 2\times\text{(the larger one)} + 7$.

$3\times\text{the smaller one} = 2\times(\text{the smaller one}+2) + 7$.

$3x = 2(x+2) + 7$

$\dots$

• I would also like to add that $x=2t+1$. Sorry about that everyone. – John Joy Nov 8 '14 at 22:14