There are 18 animals in the barnyard. There are 50 legs. How many cows and how many chickens are there in the barnyard?
Technically, I wonder if a chicken is an animal. And are chickens and cows the ONLY "animals" in the barnyard.
If we assume a chicken is an animal and that we have only chickens and cows in the barnyard, then let
X = number of chickens
Y = number of cows.
You can write two equations.
X + Y = 18 (total chickens and cows)
2X + 4Y = 50 (number of legs).
Solve for X and Y. Post your work if you get stuck.
Put your equations in the TI-83 plus put it in matrices. Go to Edit then type in where it says 1X1 put 2 X3 then type in the first equation like puting it straight across.Like 1 1 18 and then you do the second equations like you did the first equation. Then exit out then go back to matrices go to B mash go back the matrices then go to names then go to the thing that you type in mash that then mash enter again. The answer for x and y is at the end the answer to this problem is x=11 and y=7.
Put your equations in the TI-83 plus put it in matrices. Go to Edit then type in where it says 1X1 put 2 X3 then type in the first equation like puting it straight across.Like 1 1 18 and then you do the second equations like you did the first equation. Then exit out then go back to matrices go to B mash go back the matrices then go to names then go to the thing that you type in mash that then mash enter again. The answer for x and y is at the end the answer to this problem is x=11 and y=7.
To solve this problem, we can set up a system of equations. Let's assume "X" represents the number of chickens and "Y" represents the number of cows.
The first equation represents the total number of animals in the barnyard:
X + Y = 18
The second equation represents the total number of legs in the barnyard:
2X + 4Y = 50
To solve this system of equations, you can use various methods such as substitution, elimination, or matrices.
In this case, you mentioned using matrices on a TI-83 calculator. Here is the step-by-step process to solve it using matrices on a TI-83 calculator:
1. Press the "MODE" button on your calculator, then select "A+Bi" to enter the matrix mode.
2. Press the "2ND" button, then the "MODE" button to access the "Quit" menu. Select "1" to clear any previously entered data.
3. Press the "2ND" button, then the "MODE" button to access the "Quit" menu. Select "5" to return to the "MATRX" menu.
4. Press the right arrow to select "[Edit]" and press "ENTER".
5. Select a matrix you want to use (e.g., "[A]").
6. Enter the values of the first equation coefficients in a row. In this case, enter "1 1 18" (space-separated) and press "ENTER".
7. Repeat this process for the second equation. Enter "2 4 50" and press "ENTER".
8. Press the "2ND" button, then the "MATRX" button to access the "MATRX" menu.
9. Scroll down to select "[B]". Press "ENTER" to store the matrix [B].
10. Press the "2ND" button, then the "QUIT" button to exit the matrix editor.
11. Press the "2ND" button, then the "MATRX" button to access the "MATRX" menu.
12. Scroll down to select "[ALPHA]". Press "ENTER" to choose the "[ALPHA] [B] [x^-1] [ENTER]" option. This will compute the inverse of matrix [A].
13. After calculating the inverse, press the "2ND" button, then the "MATRX" button again.
14. Scroll down to select "[B]". Press "ENTER" to choose the "[ALPHA] [B] [x^-1] [ENTER]" option. This will multiply the inverse of matrix [A] by matrix [B].
15. The resulting matrix will display the solution to the system of equations. In this case, it should show "11" in the first row and "7" in the second row. Thus, the solution is X=11 and Y=7, meaning there are 11 chickens and 7 cows in the barnyard.
However, it's worth noting that in real-life scenarios, barnyards can have other animals as well, and chickens are indeed considered animals.