Certainly! Let's clarify the problem and then walk through it with a detailed, step-by-step solution on how we can form the expression for the total number of carrots that Loren and the other person can peel together in one minute.
1. Define the Variables:
- Let's denote the number of carrots Loren can peel in one minute as [tex]\( x \)[/tex].
2. Expression for the Other Person:
- Suppose the other person peels 2 fewer carrots than Loren per minute. We can denote the number of carrots this person peels as [tex]\( x - 2 \)[/tex].
3. Total Number of Carrots Peeled Together:
- To find the total number of carrots they can peel together in one minute, we need to sum the rate of carrots peeled by Loren and the rate of carrots peeled by the other person. This gives us the expression:
[tex]\[
\text{Total carrots peeled together} = \text{Number of carrots Loren can peel per minute} + \text{Number of carrots the other person can peel per minute}
\][/tex]
Substituting the variables, we get:
[tex]\[
\text{Total carrots peeled together} = x + (x - 2)
\][/tex]
4. Simplify the Expression:
- Combine the like terms in the expression:
[tex]\[
x + (x - 2) = x + x - 2 = 2x - 2
\][/tex]
5. Final Expression:
- Thus, the simplified expression for the total number of carrots Loren and the other person can peel together in one minute is:
[tex]\[
2x - 2
\][/tex]
So, the final answer is:
[tex]\[
2x - 2
\][/tex]
This represents the total number of carrots that Loren and the other person can peel together in one minute, given that Loren peels [tex]\( x \)[/tex] carrots per minute and the other person peels 2 fewer carrots per minute than Loren.
