Word problem

[Tresa332006]

I am totally not good with word problems. I do need help on this one, Please anybody.

Translate to an algebra statement; do not solve:

Three times the sum of a number and seven yields the same result as the twice the same number decreased by four.

Can anyone tell me how to set this up.

this is as far as I got and I don't even think this is right.

3(x + 7) =
Help Please

 

[tkhunny]

I am totally not good with word problems.

First, NEVER say or think that again. Learn.

Translate to an algebra statement; do not solve:

Three times the sum of a number and seven yields the same result as the twice the same number decreased by four.

Number 1 thing to do - Name things. Write down defintions and assumptions. Don't try to do it all in your head.

x = The Number

It doesn't have to be any trickier than that. Just write it down.

"sum of a number and seven"

x + 7

"Three times the sum of a number and seven"

3*(x+7)

"twice the same number decreased by four"

I think this is a bit ambiguous. It could be:

2*x - 4 or 2*(x-4)

So, we have either

3*(x+7) = 2*x - 4 or 3*(x+7) = 2*(x-4)

If it were me, I'd solve them both and see if one produces a cleaner result. That's proably the one intended.

 

[Denis]

I am totally not good with word problems. I do need help on this one, Please anybody.

Translate to an algebra statement; do not solve:

Three times the sum of a number and seven yields the same result as the twice the same number decreased by four.

Can anyone tell me how to set this up.

this is as far as I got and I don't even think this is right.

3(x + 7) =
Help Please

Start this way:
let x = the number

"Three times the sum of a number and seven"
3(x + 7) : you got that right !

"twice the same number decreased by four."
2(x - 4) : if you got the other one, what was your problem here?

3(x + 7) = 2(x - 4)
3x + 21 = 2x - 8
x = -29 : did you follow that?

You can make sure answer is correct by substituting it in both:
3(-29 + 7) = 3(-22) = -66
2(-29 - 4) = 2(-33) = -66

 

[Tresa332006]

Denis, I just was not for sure if I could do it. I had it in my head but when I went to write it on paper it didn't look right. I thank you and Tkhunny for taking time to anwer that problem you both have been a big help. thanks again.

 

[Denis]

".....the same result as twice the same number decreased by four. "

As TK told you, this could mean 2(x - 4) or 2x - 4;
make sure to tell your teacher to be clearer :wink: