Ramon ate at a restaurant and gave the server a $4 tip

Ramon ate at a restaurant and gave the server a $4 tip. The tip was 20% of the cost of the meal. How much was the meal?

A. $16

B. $20

C. $8

D. $24

Evaluate. 5:7! 6!4! Simplify your answer as much as possible.

The Correct Answer and Explanation is:

Let’s address both parts of your question in detail:

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Part 1: Tip Problem

Question:
Ramon gave a $4 tip, which was 20% of the cost of the meal. What was the total cost of the meal?

Choices:
A. $16
B. $20
C. $8
D. $24

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Step-by-Step Explanation:

The tip is a percentage of the meal cost. That means: Tip=20% of the meal cost\text{Tip} = 20\% \text{ of the meal cost}

Let the meal cost be x dollars.
Then, 0.20x=40.20x = 4

To find x, divide both sides by 0.20: x=40.20=415=4×5=20x = \frac{4}{0.20} = \frac{4}{\frac{1}{5}} = 4 \times 5 = 20

✅ Correct Answer: B. $20

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Further Explanation (300+ words):

To solve problems involving percentages, it’s helpful to convert the percentage into a decimal. Since 20% means 20 out of 100, it converts to a decimal as 0.20. The problem tells us that the tip of $4 is 20% of the meal cost, not 20% of the total amount spent (which would include the tip). This is an important distinction — sometimes questions test your understanding of “percent of what?”

The equation 0.20x = 4 reflects that 20% of the unknown meal cost x equals $4. Solving for x gives us the meal cost. Once we divide, we find that the original meal cost must have been $20, since 20% of 20 is exactly 4.

You can double-check: 0.20×20=4✔®0.20 \times 20 = 4 \quad \text{✔️}

Understanding percent problems is essential for everyday scenarios like tipping, calculating discounts, or figuring out interest. These problems often appear in standardized tests and real-world decision-making, so being comfortable with translating words into mathematical equations is key.

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Part 2: Simplify the Expression

5⋅7!6!⋅4!\frac{5 \cdot 7!}{6! \cdot 4!}

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Step-by-Step Solution:

Recall:

• 7!=7⋅6⋅5⋅4⋅3⋅2⋅17! = 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1
• 6!=6⋅5⋅4⋅3⋅2⋅16! = 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1
• 4!=4⋅3⋅2⋅14! = 4 \cdot 3 \cdot 2 \cdot 1

Now substitute: 5⋅7!6!⋅4!=5⋅(7⋅6!)6!⋅4!\frac{5 \cdot 7!}{6! \cdot 4!} = \frac{5 \cdot (7 \cdot 6!)}{6! \cdot 4!}

Cancel the 6!6!: =5⋅74!=3524= \frac{5 \cdot 7}{4!} = \frac{35}{24}

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✅ Final Simplified Answer: 3524\frac{35}{24}

This fraction cannot be simplified further because 35 and 24 have no common factors other than 1.

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