Primary 3 math question

[Ender]

Trying to help my son with this question, but was stuck. Without using simultaneous equation, hope someone good in math can help out. Can't figure out how to use model math.,

 

Question

There're total 160 ducks and pigs in the farm. Molly counted the number legs, and found that total number of legs from the pig is 100 more than the ducks.

Find out the quantity of ducks and pigs.

[The_Bear]

I am not sure but this might help...

 

Farmer Jones got out of his car and while heading for his friend's door, noticed a pig with a wooden leg. His curiosity roused, he asked, "Fred, how'd that pig get him a wooden leg?"

 

"Well, Michael, that's a mighty special pig! A while back a wild boar attacked me while I was walking in the woods. That pig there came a runnin', went after that boar and chased him away. Saved my life!"

 

"And the boar tore up his leg?"

 

"No he was fine after that. But a bit later we had that fire. Started in the shed up against the barn. Well, that ole pig started squealin' like he was stuck, woke us up, and 'fore we got out here, the darn thing had herded the other animals out of the barn and saved 'em all!"

 

"So that's when he hurt his leg, huh, Fred?"

 

"No, Michael. He was a might winded, though. When my tractor hit a rock and rolled down the hill into the pond I was knocked clean out. When I came to, that pig had dove into the pond and dragged me out 'fore I drownded. Sure did save my life."

 

"And that was when he hurt his leg?"

 

"Oh no, he was fine. Cleaned him up, too."

 

"OK, Fred. So just tell me. How did he get the wooden leg?"

 

"Well", the farmer tells him, "A pig like that, you don't want to eat all at once!"

[1fast1]

Trying to help my son with this question, but was stuck. Without using simultaneous equation, hope someone good in math can help out. Can't figure out how to use model math.,

 

Question

There're total 160 ducks and pigs in the farm. Molly counted the number legs, and found that total number of legs from the pig is 100 more than the ducks.

Find out the quantity of ducks and pigs.

 

Easy.

 

Obviously, a pig has 4 legs, a duck has 2.

 

When we count the legs of the animals, let's count the ducks' legs first (phase 1). When we're done, count the pigs' legs (phase 2).

 

After phase 1 and 2, we find that we've counted 100 more legs in phase 2. That equates to 100/4 = 25 more pigs.

 

160 - 25 = 135. That's the total number of animals so that the contribution from pig legs equals the contribution from duck legs.

 

Since the pigs have twice as many legs, we need to divide 135 in the ratio 1:2 to determine the number of pigs and ducks that are contributing to the 135 legs, respectively.

 

So no. of pigs (that contribute to 135) = 135*1/3 = 45

 

and no. of ducks = 2*45= 90

 

Total no. of pigs (add on the 25 we initially subtracted after deducing the "excess" pigs from the leg count) = 45+25 = 70.

 

So pigs = 70, ducks = 90.

Edited April 22, 2012 by Turboflat4

[1fast1]

I am not sure but this might help...

 

Farmer Jones got out of his car and while heading for his friend's door, noticed a pig with a wooden leg. His curiosity roused, he asked, "Fred, how'd that pig get him a wooden leg?"

 

"Well, Michael, that's a mighty special pig! A while back a wild boar attacked me while I was walking in the woods. That pig there came a runnin', went after that boar and chased him away. Saved my life!"

 

"And the boar tore up his leg?"

 

"No he was fine after that. But a bit later we had that fire. Started in the shed up against the barn. Well, that ole pig started squealin' like he was stuck, woke us up, and 'fore we got out here, the darn thing had herded the other animals out of the barn and saved 'em all!"

 

"So that's when he hurt his leg, huh, Fred?"

 

"No, Michael. He was a might winded, though. When my tractor hit a rock and rolled down the hill into the pond I was knocked clean out. When I came to, that pig had dove into the pond and dragged me out 'fore I drownded. Sure did save my life."

 

"And that was when he hurt his leg?"

 

"Oh no, he was fine. Cleaned him up, too."

 

"OK, Fred. So just tell me. How did he get the wooden leg?"

 

"Well", the farmer tells him, "A pig like that, you don't want to eat all at once!"

 

Awesome. I expected the farmer to start with the porker's dig bick and barge lalls first, though.

 

[Ghostrider8]

Use the guess and check for P3. Draw a table with 5 columns.

 

Start from the middle number of 160 animals, 80 pigs and 80 ducks

 

80 pigs will have 320 legs

80 ducks will have 160 legs

 

The difference is 160 legs, so this guess is incorrect.

 

Reduce or increase the legs of each animals.

 

70 pigs will have 280 legs

90 ducks will have 180 legs

the difference is 100 legs. this guess is correct.

 

There are 70 pigs and 90 Ducks.

 

 

 

[1fast1]

Use the guess and check for P3. Draw a table with 5 columns.

 

Start from the middle number of 160 animals, 80 pigs and 80 ducks

 

80 pigs will have 320 legs

80 ducks will have 160 legs

 

The difference is 160 legs, so this guess is incorrect.

 

Reduce or increase the legs of each animals.

 

70 pigs will have 280 legs

90 ducks will have 180 legs

the difference is 100 legs. this guess is correct.

 

There are 70 pigs and 90 Ducks.

 

That sounds silly, when an exact solution can easily be computed with algebra. Or with a little more difficulty using the method I posted (that reasoning might be beyond the average P3 student, though).

 

Not saying *you're* wrong or silly (so don't take offence), I'm saying the school system here sucks when they won't teach the elegance of algebra but would happily teach a crap method like "guess and check". Impressionable young kids will go away with the misapprehension that math is a bunch of random guessing.

Edited April 22, 2012 by Turboflat4

[Mcf777]

even you get the answer conrrect, teacher dont accept the guess and check way.

i aleays get knock out by such maths questions

[987]

wow, seriously... primary 3 maths???

 

if i had to go back to school once again, i'd probably stuck in primary 2...

 

tough luck for kids these days...

[Rayleigh]

Use guess and check method. This question requires two conditions to be met. The total number of animals and the 100 more legs.

 

Edited April 22, 2012 by Rayleigh

[Requiemdk]

Hmm the guess-and-check method has its merits, though not immediately obvious. To illustrate why, at the other end of the formal education timeline, too many students look at a simple problem and cannot even guesstimate a ballpark answer. It seems that students lose their intuition over time because they've been educated out of the habit of guessing/predicting (albeit reasonably). I went around for a bit asking students to give the answer to the product of 2 4-digit numbers, correct to 1 significant figure, and you'd probably despair at the number who replied that they couldn't do it without first calculating the exact answer.

[1fast1]

Hmm the guess-and-check method has its merits, though not immediately obvious. To illustrate why, at the other end of the formal education timeline, too many students look at a simple problem and cannot even guesstimate a ballpark answer. It seems that students lose their intuition over time because they've been educated out of the habit of guessing/predicting (albeit reasonably). I went around for a bit asking students to give the answer to the product of 2 4-digit numbers, correct to 1 significant figure, and you'd probably despair at the number who replied that they couldn't do it without first calculating the exact answer.

 

That is sad. But I don't believe that emphasising "guess and check" over exact methods when the latter work quickly and well, is the right thing to do. While it's important to build mathematical intuition, it's important not to give the impression that Math is wishy-washy.

 

In more sophisticated applications, sure, "guess and check" becomes acceptable. The solution to many cubics and quartics is still done in a rough and ready fashion using an iterative method like Newton-Raphson rather than using Tartaglia/Cardano's or Ferrari's exact method, because the latter are just too damn tedious. I've used Monte Carlo simulation when it was the most direct way to compute a result. And just because I understand and appreciate the theory of differential equations doesn't mean I'm not ready to whip out my Berkeley Madonna to solve some tough looking d.e.s that arise in a practical math modelling problem.

 

But the bias against "try and see" approaches is an age-old one in Math. Remember how the computer-assisted proof of the four-colour theorem wasn't fully accepted for a long time?

 

(I suspect, however, that for the most difficult open problems, this sort of approach will be inevitable. I'm guessing that the Collatz conjecture, if it's proven at all, will involve the systematic searching of a narrowed-down finite set of n-cycles. And the Riemann hypothesis may involve checking a restricted set of complex zeroes. Who knows? I'm not smart enough to solve either, but I'll accept it on faith when some genius solves either (or both!) ).

Edited April 22, 2012 by Turboflat4

[Porker]

Awesome. I expected the farmer to start with the porker's dig bick and barge lalls first, though.

 

YUCK FOU!

[1fast1]

YUCK FOU!

 

Soooo creeeever.

[Requiemdk]

To be more precise, those problems are likely to be solved by "guess and check", i.e. someone guesses, and someone else checks. No prizes for guessing who does the guessing and who does the checking

[Coltplussport]

100 more legs = 100/4 = 25 pigs

 

So the rest of 160-25 = 135 animals share equal number of leg.

 

The ratio of duck to the pigs is 2 : 1 since each pig have double the amount of each duck legs.

 

So 135/3 = 45.

 

So 45 x2 = 90 ducks

 

45+25 = 70 pigs.

[TJX]

100 more legs = 100/4 = 25 pigs

 

So the rest of 160-25 = 135 animals share equal number of leg.

 

The ratio of duck to the pigs is 2 : 1 since each pig have double the amount of each duck legs.

 

So 135/3 = 45.

 

So 45 x2 = 90 ducks

 

45+25 = 70 pigs.

 

 

clear and precise. best answer for the day.

[Wind30]

100 more legs = 100/4 = 25 pigs

 

So the rest of 160-25 = 135 animals share equal number of leg.

 

The ratio of duck to the pigs is 2 : 1 since each pig have double the amount of each duck legs.

 

So 135/3 = 45.

 

So 45 x2 = 90 ducks

 

45+25 = 70 pigs.

 

nice answer.

 

my reasoning is start with 80 pigs and 80 ducks.

 

That means pig will end up with 160 legs more than ducks which is too much. If you change one pig into a duck, you will -4 legs from pigs and + 2 to ducks which is a change of 6.

 

To reach 100, you need to -60 which means need to change 10 pigs to ducks.

 

Answer is 80-10 pigs and 80+10 ducks.

[Ender]

Thanks guys for all the answers. Especially so for the one that use ratio, which I myself have taken a lesson here too.

 

I decided to use the guess and check method for his homework, as I'm not too sure if the school teacher would approve the ratio methd yet as it's not taught to the kids in primary 3, though its a much more precise solution.