I just cant figure these kind of problems out, help!

[HelpMePlease]

Hey to all at FreeMathHelp.Com.

I have a ton of problems like the one Im about to post on here, and I just cant figure out the right way to solve them .. Im not completely sure this is the right place to post this, but hopefully someone can help me out.

Here it goes ..

The difference between two numbers is 6. If 3 times the larger number is subtracted from 52, the answer is the same as when 56 is subtracted from seven times the smaller number. Find the numbers.


These kind of problems tend to make my head expolode. I can usually figure them out by trial and error, but this one is killing me .. any good strategies on how to solve these?

any help is appreciaited.

 

[stapel]

The difference between two numbers is 6. If 3 times the larger number is subtracted from 52, the answer is the same as when 56 is subtracted from seven times the smaller number. Find the numbers.

To learn the general set-up and solution method for this sort of exercise, please try this lesson on "number" word problems. Once you've learned the basic terms and techniques, the following should make sense:

You have two numbers, and a distance between them. So pick names (that is, variables) to stand for the numbers; let's say we pick "s" for the "smaller" number and "b" for the "bigger" number.

Since the difference between the two numbers is 6, we can create an equation:

. . . . .\(\displaystyle b\, -\, s\, =\, 6\)

Create an expression, in terms of "b", for "three times the bigger number", and then create an expression for "subtracting (three times the bigger number) from 52".

Create an expression, in terms of "s", for "seven times the smaller number", and then create an expression for "subtracting 56 from (seven times the smaller number)".

Since these values are said to be the "same", you can set the two expressions equal to each other.

Since "b - s = 6" means that b = s + 6, you can replace every instance of "b" with "s + 6", and thus reduce the equation to one variable.

Solve the linear equation for the value of "s". Back-solve for the value of "b".

 

[Loren]

The difference between two numbers is 6. If 3 times the larger number is subtracted from 52, the answer is the same as when 56 is subtracted from seven times the smaller number. Find the numbers.

On all word problems, name things, and write it down. After you have them all named, locate the words that indicate the equality. That will be the equal sign. Then build your equation. If you are using two equations in two unknowns you will have to find two statements that indicate equality. I'll try to get you started.

I'm naming things now and writing them down...
Let x be the large number.
Let y be the smaller number.

The difference between two numbers is 6. The word "is" indicates equality. On one side of the = sign is "the difference between the two numbers". That would be x-y. So, I see the entire expression can be written as...

x-y=6. That's one equation. We need another equation. Let's look at the second sentence.

3 times the larger number is written as 3x.
3x is subtracted from 52 is written as 52-3x.
56 is subtracted from seven times the smaller number is written as 7y-56.
the answer is the same as <<< This is your equal sign.

Now, can you end up with two equations in two unknowns? If not, come back for more help.

OOPs! Looks like I doubled with Stapel.

 

[Denis]

These kind of problems tend to make my head expolode. I can usually figure them out by trial and error, but this one is killing me ....

ADVICE: STOP "trial and error", and learn the "method"; you won't regret it: guaranteed :wink:

 

[HelpMePlease]

Re:

The difference between two numbers is 6. If 3 times the larger number is subtracted from 52, the answer is the same as when 56 is subtracted from seven times the smaller number. Find the numbers.

To learn the general set-up and solution method for this sort of exercise, please try this lesson on "number" word problems. Once you've learned the basic terms and techniques, the following should make sense:

You have two numbers, and a distance between them. So pick names (that is, variables) to stand for the numbers; let's say we pick "s" for the "smaller" number and "b" for the "bigger" number.

Since the difference between the two numbers is 6, we can create an equation:

. . . . .\(\displaystyle b\, -\, s\, =\, 6\)

Create an expression, in terms of "b", for "three times the bigger number", and then create an expression for "subtracting (three times the bigger number) from 52".

Create an expression, in terms of "s", for "seven times the smaller number", and then create an expression for "subtracting 56 from (seven times the smaller number)".

Since these values are said to be the "same", you can set the two expressions equal to each other.

Since "b - s = 6" means that b = s + 6, you can replace every instance of "b" with "s + 6", and thus reduce the equation to one variable.

Solve the linear equation for the value of "s". Back-solve for the value of "b".

Thanks for the help guys, hopefully I can solve it now .. let me get this straight.

the equation I came up with was this:

3b-52 = 7s-56

but your saying I can make the quation :

3(s+6) - 52 = 7s - 56 ?

and just solve for S then plus it back into the old equation and find L?

 

[HelpMePlease]

I just solved the quation and I got 11.5 for the biger number and 5.5 for the smaller number, can anyone confirm this?

 

[stapel]

To check the answer to any "solving" problem, plug it back into the original exercise. Do your numbers work? If so, then your answer is right! :wink:

 

[HelpMePlease]

I came across another problem Im having some trouble with, I guess I'll just tack it on here.

Bob is now twice as old as his son. 16 years ago he was four times as old. How old is each now?

 

[Denis]

Hint:
B = 2S
B - 16 = 4(S - 16)