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Let's go through this problem step by step.

### Part (a)
The question is asking which piece of information is *not needed* to compute the bill after tax and tip. Let's analyze the options provided:

- **Option A**: "The tax was 7%" – This information is needed to compute the tax portion of the bill.
- **Option B**: "The customer left $0.90 as a tip" – This is important since it directly tells us the amount of the tip.
- **Option C**: "The customer left a 10% tip" – This is also relevant because it informs us about the tip percentage, which would be required if we were calculating the tip as a percentage of the bill.
- **Option D**: "All of this information is needed to solve the problem." – This option would mean that all the provided details are essential.

Since the customer already specified the tip amount directly as "$0.90," we don't actually need the information about the 10% tip percentage (Option C). Therefore, the correct answer for part (a) is **C. The customer left a 10% tip.**

### Part (b)
Now, let's calculate the total bill based on the given information.

Given:
1. The tip amount is $0.90.
2. The tax rate is 7%.

Let's assume the cost before tax is represented by $ x $.

The final amount after adding the tax and the fixed tip would be calculated as follows:
- The tax would add $ 0.07 \times x $.
- So, the bill including tax is $ x + 0.07x = 1.07x $.
- Adding the tip, the total bill is $ 1.07x + 0.90 $.

Since the tip is 10% of the total cost including tax, we can set up the following equation:
\[
0.10 \times 1.07x = 0.90
\]
Solving for $ x $:
\[
1.07x = 9.

A restaurant customer left $0.90 as a tip. The tax was 7% and the tip was 10% of the cost including tax.

(a) What piece of information is not needed to compute the bill after tax and tip?
(b) What was the total bill?

This problem guides students through calculating a restaurant bill with a fixed tip and tax percentage. The question focuses on essential math concepts like percentages and algebra, suitable for students in Grades 7-8.

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