Question 1175236: Hi! I have the following word problem. I'm a little confused on how to set it up to solve it. I would appreciate any help. Thank you in advance.
"Ryan Howard of the Philadelphia Phillies Ted Major League Baseball in runs batted in for the 2008 regular seasons. Josh Hamilton of the Texas Rangers, who came in second to Howard, had 16 fewer runs batted in for the 2008 regular season. Together, these two players brought home 276 runs during the 2008 regular season. How many runs batted in did Howard and Hamilton accounted for?
Found 3 solutions by ewatrrr, ikleyn, greenestamps:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
Howard + Hamilton = 276
x + (x-16) = 276
2x = 292
x = 146 Ryan Howard runs batted in. Josh Hamilton = 130 
146 + 130 = 276 checks
Wish You the Best in your Studies.
Answer by ikleyn(52809)  (Show Source):
You can put this solution on YOUR website! .
Hello, it is the American style formulating Math problems by filling them with a lot of unnecessary words.
They think that than more unnecessary words they will stuff into the text, than better --- than smarter they will seem to be . . .
Although, in reality, than more unnecessary words are in the text, than it is WORST.
Even ancient Greeks and ancient Romans just knew it . . .
So, the first task of the reader working with such problems is to CLEAN the text from this garbage.
Doing it is the necessary part of the job.
When you complete this part, the setup will become clear to you.
Now to the solution.
There are two ways to setup the problem.
First way is to use a system of two equations, if you are familiar with it.
R + J = 276 runs (together, these two players . . . )
R - J = 16 (the difference between the two . . . )
R is standing for Ryan; J is standing for Josh.
At this point, setup is completed.
To solve the system, you simply add equations and eliminate one unknown.
So, the rest is just a technique.
The other way to setup is to write
Ryan + Josh = 276
R + (R-16) = 276.
At this point, the setup is completed with one equation, and you can easily solve it.
Both ways work perfectly (as your watch at your wrist) and always produce the same result.
Which way to prefer is up to you.
For the first way to setup and to solve the problem, see numerous typical examples in my lesson
- Word problems that lead to a simple system of two equations in two unknowns
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Systems of two linear equations in two unknowns".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
Happy learning (!)
Come again to this forum soon to learn something new (!)
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
You should know and understand how to use the algebraic method for solving the problem as shown by the other tutors.
But you can get valuable exercise for your brain by solving the problem informally, using logical reasoning and mental arithmetic.
Josh H had 16 fewer RBIs than Ryan H; and the total between the two of them was 276.
Take away those 16 "extra" RBIs from Ryan's total; now the two of them have the same number, and the total is 276-16 = 260. So now each has 260/2 = 130 RBIs -- Josh 130 and Ryan 130.
Now add back the 16 you took away from Ryan to get the actual numbers: Josh 130 and Howard 130+16 = 146.
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Note that, technically, no computations at all are needed to answer the question that is asked; the answer is part of the given information:
QUESTION: "How many runs batted in did Howard AND Hamilton account for?"
ANSWER: 276
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