Answer :
Sure! Let's break down the problem step-by-step to determine which equations represent the situation described.
Problem Statement:
- Farmer Fred has a total of 139 animals.
- These include 12 horses, 45 lambs, and some cows.
- We want to find the expression for the number of cows, represented by [tex]\( c \)[/tex].
Thinking Through the Problem:
1. Calculate the number of cows, [tex]\( c \)[/tex], by considering that the total number of animals is 139. The formula to find the number of cows is:
[tex]\[
c = \text{total animals} - (\text{horses} + \text{lambs})
\][/tex]
Substituting in the numbers we have:
[tex]\[
c = 139 - (12 + 45)
\][/tex]
2. Let's simplify that formula without calculating values:
- First, add the number of horses and lambs:
[tex]\[
12 + 45 = 57
\][/tex]
- Subtract this total from the number of animals:
[tex]\[
c = 139 - 57
\][/tex]
3. Rearrange this into a valid equation. This tells us that:
[tex]\[
c = 139 - (12 + 45)
\][/tex]
4. Rewrite this to match one of the options given in the question:
[tex]\[
\text{Option}: \quad 12 + 45 + c = 139
\][/tex]
This statement reflects the total number of animals as being equal to horses plus lambs plus cows.
Valid Equations:
- The first valid equation that represents this situation is:
[tex]\[
12 + 45 + c = 139
\][/tex]
- The second valid choice, simplified, would be:
[tex]\[
c = 139 - 12 - 45
\][/tex]
Both equations correctly represent the situation where Farmer Fred has 12 horses, 45 lambs, and the remaining animals are cows, totaling 139 animals.
Therefore, the two correct equations are:
- [tex]\( 12 + 45 + c = 139 \)[/tex]
- [tex]\( c = 139 - 12 - 45 \)[/tex]
Problem Statement:
- Farmer Fred has a total of 139 animals.
- These include 12 horses, 45 lambs, and some cows.
- We want to find the expression for the number of cows, represented by [tex]\( c \)[/tex].
Thinking Through the Problem:
1. Calculate the number of cows, [tex]\( c \)[/tex], by considering that the total number of animals is 139. The formula to find the number of cows is:
[tex]\[
c = \text{total animals} - (\text{horses} + \text{lambs})
\][/tex]
Substituting in the numbers we have:
[tex]\[
c = 139 - (12 + 45)
\][/tex]
2. Let's simplify that formula without calculating values:
- First, add the number of horses and lambs:
[tex]\[
12 + 45 = 57
\][/tex]
- Subtract this total from the number of animals:
[tex]\[
c = 139 - 57
\][/tex]
3. Rearrange this into a valid equation. This tells us that:
[tex]\[
c = 139 - (12 + 45)
\][/tex]
4. Rewrite this to match one of the options given in the question:
[tex]\[
\text{Option}: \quad 12 + 45 + c = 139
\][/tex]
This statement reflects the total number of animals as being equal to horses plus lambs plus cows.
Valid Equations:
- The first valid equation that represents this situation is:
[tex]\[
12 + 45 + c = 139
\][/tex]
- The second valid choice, simplified, would be:
[tex]\[
c = 139 - 12 - 45
\][/tex]
Both equations correctly represent the situation where Farmer Fred has 12 horses, 45 lambs, and the remaining animals are cows, totaling 139 animals.
Therefore, the two correct equations are:
- [tex]\( 12 + 45 + c = 139 \)[/tex]
- [tex]\( c = 139 - 12 - 45 \)[/tex]
