1. ## word problem

I can't figure out how to write this problem out, so that I can solve it. Here it is: Three times a certain number is as much less than 55 as 4 times the number exceeds 50. What is the number? Can someone help me please? Thanks.

2. Originally Posted by jesuslover
I can't figure out how to write this problem out, so that I can solve it. Here it is: Three times a certain number is as much less than 55 as 4 times the number exceeds 50. What is the number? Can someone help me please? Thanks.
What does "as much less than" mean? Perhaps, if you reworded your problem, then we can answer you. This is the best I could come up with:

$\displaystyle 55-3x = 4x-50$

$\displaystyle x = \frac{105}{7} \Rightarrow x = 15$

3. Originally Posted by jesuslover
I can't figure out how to write this problem out, so that I can solve it. Here it is: Three times a certain number is as much less than 55 as 4 times the number exceeds 50. What is the number? Can someone help me please? Thanks.
Let the number be $\displaystyle x$

then the amount that three times the number is less than 55 is: $\displaystyle 55 - 3x$

and the amount that 4 times the number exceeds 50 is: $\displaystyle 4x - 50$

we are told these are the same, that is: $\displaystyle 55 - 3x = 4x - 50$

now solve for $\displaystyle x$

EDIT: Ah, Colby beat me to it and did it for you

4. Originally Posted by jesuslover
I can't figure out how to write this problem out, so that I can solve it. Here it is: Three times a certain number is as much less than 55 as 4 times the number exceeds 50. What is the number? Can someone help me please? Thanks.
It's also interesting to note that you could interpret the 'amount less' or the 'amount exceeding' as negative values $\displaystyle \Rightarrow 3x>55$ and $\displaystyle 50>4x$ so you get

$\displaystyle 3x-55=50-4x$

But this still gets you to $\displaystyle x = 15$

Note that you cannot allow the 'amount 3x is less than 55' and the 'amount 4x exceeds 55' to alternate in sign, as this would lead to the incorrect equations:

$\displaystyle 3x-55=4x-50$ or $\displaystyle 55-3x=50-4x$

As the LHS's sign is not equal to the RHS's sign, this cannot be possible.

5. Hello, jesuslover!

Sometimes, "baby talk" will help . . .

Three times a certain number is as much less than 55
as 4 times the number exceeds 50.
What is the number?

Let $\displaystyle x$ = the number.

"Three times $\displaystyle x$ is as much less than 55" tells us that $\displaystyle 3x$ is less than 55.
How much less?
. . The difference is: .$\displaystyle 55-3x$

"Four times number exceeds 50" tells us that $\displaystyle 4x$ is greater than 50.
How much more?
. . The amount is: .$\displaystyle 4x - 50$

We are told that these amounts are equal.

. . There is our equation! . $\displaystyle 55-3x \:=\:4x-50$

Go for it!

6. Thank-you. I had 3n-55 =4n+50, which didn't come out right. I see where I messed up. Thanks a lot.

7. man, we're really beating this problem to death aren't we?

8. Originally Posted by Jhevon
man, we're really beating this problem to death aren't we?
It seems that it's a race to get to every question first.