A farmer collected some eggs from his farm and found b eggs broken. He packed the remaining eggs in c egg cartons. Each egg carton can hold a dozen eggs and no eggs were leftover. Write an algebraic expression for the number of eggs he collected initially in terms of b and c.
Let's crack this problem with a little algebraic humor! The number of eggs the farmer collected initially can be expressed as:
12c + b
Why? Well, think about it. The farmer packed the remaining eggs in c egg cartons, and each carton can hold a dozen eggs (that's 12 in case you missed the pun). So, we have 12c.
But wait, there's more! The farmer also found b eggs broken, which we need to add to the total. And there you have it, the algebraic expression for the number of eggs collected initially: 12c + b. Now that's an egg-cellent solution, don't you think?
Let's break down the problem step by step:
Step 1: Calculate the number of eggs in each egg carton
Since each egg carton can hold a dozen eggs, there are 12 eggs in each carton.
Step 2: Calculate the total number of eggs in all the cartons
The number of eggs in all the cartons is given by c multiplied by the number of eggs in each carton, which is 12. So the total number of eggs in all the cartons is 12c.
Step 3: Calculate the number of broken eggs
The farmer found b eggs broken.
Step 4: Calculate the number of eggs collected initially
To calculate the number of eggs collected initially, we need to add the number of broken eggs (b) to the number of eggs in all the cartons (12c). So the expression for the number of eggs collected initially in terms of b and c is:
Total eggs collected initially = 12c + b
Therefore, the algebraic expression for the number of eggs the farmer collected initially in terms of b and c is 12c + b.
Let's break down the problem step by step to derive the algebraic expression:
1. The farmer collected some eggs from his farm.
Let's assume that the number of eggs the farmer collected initially is represented by the variable "x".
2. Out of these collected eggs, b eggs were found broken.
Therefore, the number of eggs remaining after some were broken would be x - b.
3. The remaining eggs were packed into c egg cartons.
Each egg carton can hold a dozen eggs, which is equivalent to 12 eggs.
So, the number of eggs packed into c cartons would be 12c.
Therefore, the final algebraic expression for the number of eggs the farmer collected initially in terms of b and c is:
x - b = 12c.
Note that since we don't have enough information in the problem statement to determine the exact value of x, we can only express it in terms of the number of broken eggs (b) and the number of egg cartons used (c).