Let's tackle each part of the problem systematically.

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1. Evaluating expressions to find the greatest value

a) $5(3) - 2 + 8$
$5(3) = 15 \quad \Rightarrow \quad 15 - 2 + 8 = 21$

b) $5 + 3(2) + 8$
$3(2) = 6 \quad \Rightarrow \quad 5 + 6 + 8 = 19$

c) $5 - 3 + (2 + 8)$
$2 + 8 = 10 \quad \Rightarrow \quad 5 - 3 + 10 = 12$

Greatest value: $a = 21$.

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2. Total customers served

If 40% of the customers ordered burritos and 280 customers ordered burritos:
$280 = 0.40 \times \text{Total Customers}$ $\text{Total Customers} = \frac{280}{0.40} = 700$

Total customers served: 700.

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3. Shading 38% of the grid

If the grid contains 100 squares, to shade 38%, you shade: $38 \, \text{squares}.$

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4. Driving time

If 25 minutes is needed to drive 35 miles: $\text{Rate} = \frac{\text{Distance}}{\text{Time}} = \frac{35}{25} = 1.4 \, \text{miles/minute}.$ For 70 miles: $\text{Time} = \frac{\text{Distance}}{\text{Rate}} = \frac{70}{1.4} = 50 \, \text{minutes}.$

Time to drive 70 miles: 50 minutes.

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5. Cost per eraser

If 20 erasers cost $1: $\text{Cost per eraser} = \frac{1}{20} = 0.05 \, \text{dollars} \, \text{(5 cents per eraser)}.$

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6. Percent scores

For History: $\text{Percent} = \frac{18}{20} \times 100 = 90\%.$

For Science: $\text{Percent} = \frac{22}{25} \times 100 = 88\%.$

History: 90%
Science: 88%

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7. Percent of the grid shaded

If 38 squares are shaded in a 100-square grid: $\text{Percent shaded} = \frac{38}{100} \times 100 = 38\%.$

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If you have any specific questions about these solutions or want me to explain a particular part, feel free to ask! 😊

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Relative Questions:

1. How would the greatest expression change if one term was altered?
2. What is the significance of understanding percentages in real-world situations like customer data?
3. Can we determine the cost of 50 erasers given the same price rate?
4. How would travel time change if the speed was increased by 20%?
5. Why is it useful to compare scores using percentages?

Tip: When solving multi-step problems, follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) to ensure accuracy.