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------------------------------------------------ Write an equation. Is the given value a solution?

A farmer sees 56 of his cows out of the barn. He knows that he has 83 cows altogether. Let [tex]c[/tex] represent the number of cows still in the barn. Could [tex]c=33[/tex]?

A. [tex]83+c=56[/tex]; no
B. [tex]c+33=56[/tex]; yes
C. [tex]56+c=83[/tex]; no
D. [tex]56+83=c[/tex]; no

Answer :

To solve the problem, we need to set up an equation based on the information given and check if the value [tex]\( c = 33 \)[/tex] is a solution.

1. Understanding the problem:
- The farmer has a total of 83 cows.
- There are 56 cows outside of the barn.
- We need to find how many cows are still in the barn, represented by [tex]\( c \)[/tex].

2. Setting up the equation:
- Since the total number of cows is 83, and 56 are outside, the cows inside the barn can be represented by:
[tex]\[ 83 - 56 = c \][/tex]

3. Calculate the number of cows inside the barn:
- Subtract the number of outside cows from the total number of cows:
[tex]\[ 83 - 56 = 27 \][/tex]
- This means there are 27 cows inside the barn.

4. Check if [tex]\( c = 33 \)[/tex] is a solution:
- We found that there are 27 cows inside the barn, so let’s see if 33 could be the number of cows inside:
- Since 27 is not equal to 33, [tex]\( c = 33 \)[/tex] is not a solution.

Therefore, the given value [tex]\( c = 33 \)[/tex] is not a solution to the equation. The correct answer for the number of cows still in the barn is 27, and the value [tex]\( c = 33 \)[/tex] is not a solution.