# Algrbra Problem My Daughter and I are stuck on

#### keith075

##### New member
My daughter is just starting out in algebra and on a take home test she received a bonus problem that had not been covered in the material (hence, I assume why the teacher makes it a bonus). I can figure out the answer through process of elimination but I can not figure out what the actual formula would be to solve it and that is what gives the actual bonus points. Any help would be appreciated...here's the question-

On a farm there are horses and three legged cows. There are a total of 131 heads and 486 legs. How many horses are on the farm?

I figured out there were 93 horses by using plugging in vairables of 131 then multiplying them out by the legs...someone please show us how we should have properly found the answer. I should know this...my mind is this close <makes small hand gesture> to figuring it out but I'm still in the dark.

#### wjm11

##### Senior Member
On a farm there are horses and three legged cows. There are a total of 131 heads and 486 legs. How many horses are on the farm?
Assign variables:
H = number of horses
C = number of three-legged cows

H + C = 131
4H + 3C = 486

You now have two equations and two unknowns. Just solve the system of equations.

#### Subhotosh Khan

##### Super Moderator
Staff member
keith075 said:
My daughter is just starting out in algebra and on a take home test she received a bonus problem that had not been covered in the material (hence, I assume why the teacher makes it a bonus). I can figure out the answer through process of elimination but I can not figure out what the actual formula would be to solve it and that is what gives the actual bonus points. Any help would be appreciated...here's the question-

On a farm there are horses and three legged cows. There are a total of 131 heads and 486 legs. How many horses are on the farm?

I figured out there were 93 horses by using plugging in vairables of 131 then multiplying them out by the legs...someone please show us how we should have properly found the answer. I should know this...my mind is this close <makes small hand gesture> to figuring it out but I'm still in the dark.
There is another way - educated trial & error

Let us assume there are 65 horses and 66 cows - then we have 458 legs. We need (486-458 =) 28 more legs.

For swapping 1 cow with one horse we gain 1 leg.

So we have (65+28 = ) 93 horses and (66 - 28 =)38 cows.

Now check # of legs and heads again for correctness.

#### keith075

##### New member
Thanks guys..I remember now. I was trying to work both formulas into one without eliminating either the C or the H beforehand. With your help, it now makes sense-

H+C=131
C=131-H

then-

4H + 3(131-H) = 486
4H + 393 - 3H = 486
H + 393 = 486
H = 93

then finally-

93 + C = 131
C = 38

I've been out of the Algebra world for too long. I enoyed the challenge and really appreciate the help!

#### Mrspi

##### Senior Member
So...who gets the "bonus" points? Your daughter? I don't think so.

You? Maybe.

This is why I will not give answers to "test questions"....ESPECIALLY if it is a parent who asks for the answer.

#### keith075

##### New member
Should I have punished my kid for spending time over the three day break getting the correct answer? She's in 5th grade and in my opinion the problem was too hard to begin with....all I did was provide the formula after she knew the correct answer.

Remember, the answer was included in my original post...we both knew that without the formula. If she did not get the answer I still would have given her the formula because they're doing problems on the test like x-3=12 (no double variables yet...that's why it was extra credit), but I would not have outright handed her the answer. I checked her test and she missed 2 out of 20, told her to recheck the entire page and it went down to 1 wrong of 20....she had an A either way.

Now she has an A and probably is the only one in the class who can solve a problem with 2 variables....I see nothing wrong with that. Like I said.....a 5th grader solving a problem like this is very good and in my opinion parents should make their kids strive towards learning.

#### mmm4444bot

##### Super Moderator
Staff member
Keith:

The correct solution to the bonus question is boring. The interesting part is how people arrive at a solution, correct or incorrect. The entire point is to get students thinking. (If your daughter had come up with something like a process of elimination, I'm confident that she would have received some bonus points for that.)

I understand your stated opinion that this question is "too hard" for a bonus question. It seems to me that you've missed the point.

Also, your claim that your daughter is likely the only student in her class who can solve a problem with 2 variables after being shown how to do it is diminished.

Most people can do a thing, after it's been explained.

You should be commended for pushing your daughter to learn and succeed. Heck, you should be commended simply for being involved, since many parents are MIA.

Should you punish your daughter? No.

But, if you allow your daughter to turn in a solution to a bonus question on a take-home test without clearly indicating to the instructor that which belongs to your daughter's independent thinking versus that which you and the Internet achieved, then you should punish yourself for setting a bad example with respect to academic integrity.

Cheers ~ Mark

#### Mrspi

##### Senior Member

Had I known that, I'd have had a different perspective on the problem.

"Problem solving" is a big topic in the middle grades...4th-6th

"Guess and check" is a very valid problem-solving technique, and one that is stressed at this level.

I'm wondering if "algebraic solution" is YOUR interpretation of what the teacher wants. I'm guessing that at the 5th grade level, an algebraic solution, ESPECIALLY one which involves a system of two equations in two variables, is not what the teacher is looking for.

I'm pretty sure that the teacher is NOT looking for what DAD found on the internet.

That's just my perspective, and I'm sure it isn't anything you want to hear.

#### Denis

##### Senior Member
keith075 said:
On a farm there are horses and three legged cows. There are a total of 131 heads and 486 legs. How many horses are on the farm?

I got the answer (93 horses) by trial and error. Could someone show me how to solve using algebra?
C'mon ya'll, give poor Dad a break!
Keith could have simply posted what I show above.
After all, he did state that HE IS THE ONE WHO FORGOT...

#### mmm4444bot

##### Super Moderator
Staff member
Denis said:
C'mon ya'll, give poor Dad a break!

You just did, but okay:

As long as the teacher is privy to what went down on this TEST, it's all good.

#### Denis

##### Senior Member
Agree.
Keith's daughter will at one point learn how to handle equations with 2 variables:
who cares if she learns from her Dad, or by Googling, of from her teacher....?

#### chrisr

##### Full Member
Can i join your fan club now, Denis ?

#### Denis

##### Senior Member
chrisr said:
Can i join your fan club now, Denis ?
I'll have my brother-in-law (who owes me \$1,200 and is the only present member...and treasurer)
contact you; hope you deal with PayPal :idea: