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3. Sam's farm has cows and chickens. If he was a total of 35 cows and chickens and a total of 104 legs.

How many cows and chickens are on his farm?

a. Write the system of equations. Be sure to define your variables.

b. Solve.

User Jimbali
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1 Answer

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Answer:

17 cows and 18 chickens

Explanation:

let x equal the number of cows. (cows have 4 legs)

let y equal the number of chickens. (chickens have 2 legs)

a. x+y=35

4x+2y=104

b. Let's use substitution. This means that we'll solve for a variable in one equation in terms of the other and then substitute that into our second equation, then backtrack to find the second variable.
How about we solve for x in terms of y in the first equation? Well, then we have x=35-y. Now let's substitute that into the second equation!
4(35-y)+2y=104. Distribute the 4 to get 140-4y+2y=104. Combine like terms to get 140-2y=104 and isolate the variable: -2y=104-140, or -2y=-36. Isolate y further to obtain y=18.

Now we can take our new y-value and go back to the first equation. So, x+18=35. Isolate x to get x=35-18, or x=17.

Finally, let's check our work by substituting x and y into our original system.

17+18=35 (works!)

4(17)+2(18)=104 (also works!)
Since both equations work, our solution works.

User WoodenKitty
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