Word Algebra Problem

• Nov 11th 2011, 03:35 PM
Hellbent
Word Algebra Problem
Hi!

J'onn J'onnz worked 7 more problems than Clark Kent. Together they worked 55 problems. How many did each boy work?

I got 31 for J'onn and 24 for Clark:

J'onn = J
Clark = C

J = 7 + C
7 + C = 55
C = 48

48/2 = 24 ==> Clark
24 + 7 = 31 ==> J'onn

Another way is: 55 + 7 = 62
62/2 = 31
31 - 7 = 24

I think my methods are flawed and that's the reason for my seeking help.
• Nov 11th 2011, 03:41 PM
Quacky
Re: Word Algebra Problem
I don't understand the method. It may be correct and valid, I just don't understand it.

I agree with \$\displaystyle J=7+C\$

Together they worked \$\displaystyle 55\$ problems.
So:

\$\displaystyle J+C=55\$

We have two equations:
\$\displaystyle J=7+C\$
\$\displaystyle J+C=55\$

I'd substitute the first into the second, to get:
\$\displaystyle (7+C)+C=55\$
• Nov 11th 2011, 07:49 PM
mathbyte
Re: Word Algebra Problem
One more point to what Quacky said:
You were asked the question "how many problems did each boy work?"
By that question being asked, you know there are two unknowns to find.
For x unknowns, you need x equations to solve for them.
Thus, for two unknowns, you need to establish two equations based on the given information to find them.
Once you have the same number of equations as unknowns, you can then start to solve the problem. Quacky suggested substituting one equation into the other one and that's definitely your best bet.
• Nov 12th 2011, 11:33 AM
HallsofIvy
Re: Word Algebra Problem
Quote:

Originally Posted by Hellbent
Hi!

J'onn J'onnz worked 7 more problems than Clark Kent. Together they worked 55 problems. How many did each boy work?

I got 31 for J'onn and 24 for Clark:

J'onn = J
Clark = C

J = 7 + C
7 + C = 55

No, J+ C= 55 so (7+ C)+ C= 7+ 2C= 55

Quote:

C = 48
No, 2C= 48 so C= 48/2= 24

Quote:

48/2 = 24 ==> Clark
Okay, now you have the correct value- but you had said before "Clark = C" by which I assume you meant that C was the number of problems Clark worked. Having said that, it makes no sense to say "7+ C= 55" or to divide C by 2 to get the number of problems Clark worked.

Quote:

24 + 7 = 31 ==> J'onn

Another way is: 55 + 7 = 62
Why? What part of the statement of this problem leads you to add 7 to 62?
Quote:

62/2 = 31

31 - 7 = 24

I think my methods are flawed and that's the reason for my seeking help.
You do come to the correct answer but what logic led you to it?

It is true that if J= 7+ C so C= J- 7. Then J+ C= J+ J- 7= 2J- 7= 55. Now you have that 2J= 55+ 7= 62 and then J= 31. If that was your reasoning, great- but say so!