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# Maths's problem solving

I used to be really good with maths, but after my camping accident I cannot remember most of the things.  Even the simply maths' problem solving I find it hard to teach my kid how to solve it.  I need some help and guide here please.  The question is like this:

Mike has only ducks and cows on his farm. The cows and ducks have 52 legs in total. There are 4 more cows than ducks on mike's farm how many Ducks are there on mike's farm?

How can I explain it to my kid. I know it is really easy but somehow my brain just won't function. Thank you kindly for your help and time.

Needed help urgently.

Desperate mum

Well, we know enough information to make some equations and solve them.

Things we know:

1) 52 legs total

2) Ducks have 2 legs

3) Cows have 4 legs

4) No other legs are being counted

5) 4 more cows than ducks

We have 2 unknowns: # of ducks, we'll call that D, and # of cows, we'll call that C.

So from facts 1 through 4 we can say that duck legs + cow legs = 52.  Each duck has 2 legs and each cow has 4 legs.  Therefore, we can write:

Equation 1: 2D + 4C = 52 (2 legs for each duck and 4 legs for each cow is 52 legs total)

From fact #5 we know that: C = D + 4.  This is equation 2.

We have 2 equations and 2 unknowns so we can solve it.

From there you solve the equations using substitution.  Take equation 2 and put "D+4" in place of "C" in equation 1.

Equation 1: 2D + 4C = 52

Substitute in "D + 4" for "C"

2D + 4(D + 4) = 52

Multiply the 4 through:

2D + 4D + 16 = 52

6D + 16 = 52

Subtract 16 from both sides to get D on one side.

6D = 36

Divide by 6 to find D

D = 6

There are 6 ducks.

The problem doesn't ask for # of cows, but we know this too now.  C = D + 4 so there are 10 cows.

You can easily do a quick check now.  10 cows with 4 legs each is 40 legs.  6 ducks with 2 legs each is 12 legs.  40 + 12 is 52 which is correct.

Hello Karmen -- I'm very sorry you've suffered an accident.  Here's another approach:

Start with all cows, no ducks -- 13 cows with 4 legs each.

One less cow must be replaced with 2 ducks to remain with 52 legs:

12c+2d, 11c+4d, 10c+6d ==> Answer is 10 cows and 6 ducks ... Best wishes to you & your child :)