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Maths's problem solving

Dear Sir/Madam, 

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

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2 Answers

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

Add your D terms

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 :)