Alexa bought treats for her dog. She gave her dog 2 treats on Tuesday, 0 treats on Wednesday, and 3 treats on Thursday. On Friday, she gave her dog one third of the remaining treats. If the expression 3t + 5 represents the total number of treats that Alexa purchased, what is t? 

Let's solve the problem step by step.

The total number of treats Alexa purchased is given by the expression \( 3t + 5 \).

### Step 1: Determine the initial number of treats.
The expression \( 3t + 5 \) represents the total number of treats. 

### Step 2: Calculate the treats given before Friday.
Alexa gave:
- 2 treats on Tuesday,
- 0 treats on Wednesday,
- 3 treats on Thursday.

So, the total number of treats given before Friday is:
\[
2 + 0 + 3 = 5 \text{ treats}
\]

### Step 3: Determine the remaining treats on Friday.
After giving away 5 treats, the remaining treats would be:
\[
(3t + 5) - 5 = 3t \text{ treats}
\]

### Step 4: Calculate the number of treats given on Friday.
On Friday, Alexa gave her dog one third of the remaining treats, which is:
\[
\frac{1}{3} \times 3t = t \text{ treats}
\]

### Step 5: Set up the equation for the number of treats given.
According to the problem, the number of treats given on Friday is \( t \). Since this \( t \) represents the number of treats given on Friday, and we previously found that this equals the expression \( t \) itself, we set up the equation:
\[
t = t
\]

### Step 6: Solve the equation.
There is no need to solve \( t = t \) further, as it is already a balanced equation. However, to solve for \( t \), we revisit the total treats expression \( 3t + 5 \) and relate it to the treats given.

To solve for \( t \), notice that all treats have been accounted for in the given days. Since there are no inconsistencies, \( t \) can be any value that satisfies the equation.

Given no extra condition has been provided, the value of \( t \) is:

\[
t = 0
\]

Thus, \( t \) is 0.

Would you like more details on any part of this solution? Here are some related questions to explore:

1. How would the solution change if Alexa gave away more treats on Wednesday?
2. What would happen if she gave half the remaining treats on Friday instead of one third?
3. Can we calculate how many treats were left after Friday?
4. What if the expression for total treats was different, like \(4t + 7\)?
5. How can we verify if there was a mistake in our calculations?
6. What if Alexa gave 2t treats on Friday? How would that affect the solution?
7. Could there be a different value for \( t \) if the treats given on Friday weren't specified?
8. How do we handle similar problems involving fractions of quantities?

**Tip:** Always double-check which variable represents what in word problems to avoid misinterpretation.

Learn how to solve the problem of treats distribution by Alexa, where she gave treats to her dog on different days and then distributed treats on Friday. Understand the equation 3t + 5 and find the value of t. Suitable for students in Grades 6-8.

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