How bout this one... it's a tuffy!!

[KristaB.]

Sooo, this one is like, uber confusing. Anyone wanna take a stab at it??

The difference between a number and 9 is the same as 49 less the number. Find it.

I'm stumped!! :roll:

 

[stapel]

Pick a variable for "a number".

Form the difference between this variable and 9.

Write an expression for "49 less than" the number.

Take the given relationship:

. . . . .(difference between a number and 9) is (49 less than the number)

Translate this into an equation using the expressions you have creating, remembering that "is" means "equals".

Solve for the variable.

If you get stuck, please reply showing how far you have gotten in following these instructions. Thank you.

Eliz.

 

[KristaB.]

so what you're saying is...

x-9 = 49-x ..... right?

How would I begin to figure out what the number is? Would I add 9 on both sides, cancelling it out on the left and giving me 58 on the right... ? Or am I completely off?

 

[soroban]

Hello, KristaB.!

The difference between a number and 9 is the same as 49 less the number. Find it.

Let \(\displaystyle x\) be the number.

"49 less than \(\displaystyle x\)" is \(\displaystyle x\,-\,49\)

But the "difference between \(\displaystyle x\) and 9" could be either: \(\displaystyle x\,-\,9\) or \(\displaystyle 9\,-\,x\)

We'll try it both ways . . .

[1] \(\displaystyle \;x\,-\,9\:=\:x\,-\,49\;\;\Rightarrow\;\;-9\,=\,-49\;???\)

[2] \(\displaystyle \;9\,-\,x\:=\:x\,-\,49\;\;\Rightarrow\;\;-2x\,=\,-58\;\;\Rightarrow\;\;x\,=\,29\) . . . there!

 

[KristaB.]

!!!

wow!! i didn't think of doing it that way!! you're the best, soroban!!

 

[stapel]

...the "difference between \(\displaystyle x\) and 9" could be either: \(\displaystyle x\,-\,9\) or \(\displaystyle 9\,-\,x\)

"The difference between this and that" is customarily taken to mean "(this) - (that)". In other words, subtract in the order given.

Eliz.

 

[KristaB.]

yeah i already got it, thanks to soroban.