Math Help Please!!!

[jama]

Can anyone show my ds12 how to solve the following problem? We can get the correct answer by just multiplying numbers but have no idea of a formula to show the work.
here is the problem:

In a pasture there are ducks and cows. If there are 46 heads and 124 legs then how many ducks and how many cows are there?

Thanks!

 

[jama]

can anyone do this problem?

 

[jwsqrdplus2]

If I remember my algerbra correctly:

Let x = the number of ducks
Let y = the number of cows

So:

x + y = 24
(animals)

and

2x + 4y = 124
(legs)

Next step:

x = 24 - y

so

2(24 - y) + 4y = 124

solve from there

 

[EthansMom]

In a pasture there are ducks and cows. If there are 46 heads and 124 legs then how many ducks and how many cows are there?

D = # of ducks
C = # of cows

Each duck has 2 legs and each cow has 4 legs, so:

2D + 4C = 124

Each duck has one head and each cow has one head, so:

D + C = 46


You can then use the two formulas to solve for D and C.

D + C = 46
D + C - C = 46 - C
D = 46 - C

2D + 4C = 124
plug in D from above to get
2(46-C) + 4C = 124
92 - 2C + 4C = 124
92 + 2C = 124
92 + 2C - 92 = 124 - 92
2C = 32
C = 16 cows

plug value for C into formula above:

D + C = 46
D + 16 = 46
D + 16 - 16 = 46 - 16
D = 30 ducks

I hope this helps!

 

[jwsqrdplus2]

EthansMom, glad to know my math skills are still there! I guess I'm gonna need them when my girls get older!

 

[EthansMom]

EthansMom, glad to know my math skills are still there! I guess I'm gonna need them when my girls get older!

I can handle the algebra, but I'm going to need to seriously brush up when it's time for Trig. and Calculus. Thankfully, DH still uses his Calc. every day at work (he's and Engineer who does mathematical analysis every day), so our kids will be set when it comes to homework help!

 

[Lisa loves Pooh]

But who used a graphic calculator?

 

[EthansMom]

But who used a graphic calculator?

No calculator was purchased for the solving of this problem!

 

[jama]

THANKS!!!
It looks so easy now you explained it!

 

[EthansMom]

You're welcome!

 

[Sleepy]

My son and I had a similar math problem in the algebra book. The concept for solving was more guess and check with no real "formula" to use. You just picked a number by guessing, see if you were right, then changed the answer as you saw fit until it was correct.