Need help with transation of Mathematical sentences

[godslight62]

OK I am having major problems understanding how to convert a simultaneous equation. This is probably going to be very simple to most of you but here is the sentence, Ralph and Sam caught 22 fish. If Sam had caught two more, he would have caught twice as many as Ralph. How many fish did each one catch? I have tried every mathematical equation to figure this out and every way I go I hit a dead end. Please help me with this one or I fear I will have to start the whole chapter all over again. BTW the book gave no example one word problems with the wording used in this problem and I know all my mathematical symbols by memory but this has me stumped! :yuck:

 

[Hootenanny]

Hi there godslight62 and welcome to PF,

Just for future reference there is a https://www.physicsforums.com/forumdisplay.php?f=152" where your can post your homework questions. As for your question, from the prose you can extract two equations. Start by letting R be the number of fish caught by Ralph and S be the number of fish caught by Sam. Now, you know that together they both caught 22 fish; therefore, the first equation your can write is;

$$R + S = 22$$

Now, using this section of text;

If Sam had caught two more, he would have caught twice as many as Ralph

Can you think of another equation you can write?

 

[HallsofIvy]

First rule NAME THINGS!

"Let S be the number of fish Sam caught and let R be the number of fish Ralph caught".

Although it is perfectly alright to use "x", "y", etc., I find that using letters connected to the problem (as "S" for "Sam's fish") helps me keep track of them. It is also a good idea to explicetely write out a full sentence like that. (Anyway, it will amaze and impress your teacher!)

Once that is done, every sentence corresponds to an equation.
"Ralph and Sam caught 22 fish." That is the total they caught together was 22. Of course if you knew how much each caught, you would find the total by adding: since Sam caught S fish and Ralph caught R, together they caught R+ S. "Ralph and Sam caught 22 fish" is exactly the same as "R+ S= 22".

" If Sam had caught two more, he would have caught twice as many as Ralph."
Same caught S fish. If he had caught 2 more, he would have caught S+ 2. Ralph caught R fish. "Twice as many" would be 2R. "If Sam had caught two more, he would have caught twices as many as Ralph" tells you those are equal: S+ 2= 2R.

 

[godslight62]

Thank you Hootenanny and HallofIvy.
I appreiciate your help, and in the future I will go to the homework link, thanks for letting me know.