Singapore Challenging word problem --Need Help

[Blossom'sGirl]

This is in the level 4 book. I think I can do it algebraically ,but I need the modeling approach. Here it is ...

There are three times as many ducks as sheep on a farm. All the ducks and sheep have 2400 feet altogether. How many more ducks than sheep are there?

I sure the answer is right in front of me but my model isn't working.

[Janet in Toronto]

Ducks: 1-----1-----1-----1
Sheep: 1-----1

Now we need to translate this into "feet. Sheep have twice as many feet as ducks, so the new diagram is:

Duck Feet: 1------1------1------1
Sheep Feet: 1------1------1

If there are 2400 feet altogether, and 5 feet "units", then each unit is 480.

That means that there are 1440(=3x480) duck feet and 760(=2x480) sheep feet.

So there are 720 ducks and 190 sheep.

So there are 720-190=530 more ducks than sheep.

I'm doing the arithmetic in my head, but I think the process is correct.

Janet in Toronto

[Blossom'sGirl]

Your model works except that 480*2= 960 not 760. Using these numbers you get the correct answer which is 480.

Thanks so much. Now I get to explain it to 9yo.

[Janet in Toronto]

D'Oh! like I said, I did the arithmetic in my head (and while watching Oprah!).

Peace.

Janet

[mtnparent]

There are three times as many ducks as sheep on a farm. All the ducks and sheep have 2400 feet altogether. How many more ducks than sheep are there?

Ducks XXX XXX XXX
2 2 2

Sheep XXX
4
(I can't get this to format correctly..but for each unit of ducks you have 2 feet and for each unit of sheep you have 4 feet)



I can see that for every 6 duck feet I have 4 sheep feet for a ratio of 6:4. That means I have 10 parts to the ratio which share the 2400. 2400/10 = 240.

Therefore duck feet equal 240 X 6 (from the ratio) = 1440

Sheep feet 4 X 240 = 960

Check 960 + 1440 = 2400.

Then divide the duck feet by 2 to get total ducks. 1440/2 = 720

Then divide sheep feet by 4 to get total sheep. 960/4 = 240.

The difference between ducks and sheep is 480.

[Blossom'sGirl]

We have not covered ratios yet but I tried doing it this way earlier just to solve it myself and I could not get it straight in my head. I like your solution.

My dh called with another solution from work and he basically turned it an algebra equation. He is not really into the modeling approach no matter how much I try to explain it to him.

Thanks