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Which situation matches the inequality 10x > 8x + 10?

Option 1: Valeria charges $8 an hour for babysitting. Daniel charges $10 per hour plus a traveling fee of $8. How many hours does Valeria need to babysit to make more money than Daniel?
Option 2: Valeria charges $10 an hour for babysitting. Daniel charges $10 per hour plus a traveling fee of $8. How many hours does Valeria need to babysit to make more money than Daniel?
Option 3: Valeria charges $10 an hour for babysitting. Daniel charges $8 per hour plus a traveling fee of $10. How many hours does Valeria need to babysit to make more money than Daniel?

User Kyungjin
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1 Answer

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Final answer:

To find the situation that matches the inequality 10x > 8x + 10, we compare the earnings of Valeria and Daniel. Option 1, where Valeria charges $8 an hour and Daniel charges $10 per hour plus a traveling fee of $8, matches the inequality when Valeria babysits for more than 5 hours.

Step-by-step explanation:

The inequality given is 10x > 8x + 10. To find which situation matches this inequality, we need to compare the earnings of Valeria and Daniel. Option 1 states that Valeria charges $8 an hour for babysitting and Daniel charges $10 per hour plus a traveling fee of $8. Let's calculate the earnings of both:

Valeria: Earnings = 8x (assuming x hours)

Daniel: Earnings = 10x + 8

Now we need to find the number of hours (x) for which Valeria's earnings are greater than Daniel's earnings. Let's solve the inequality:

10x > 8x + 10

Subtracting 8x from both sides: 2x > 10

Dividing both sides by 2: x > 5

So, Valeria needs to babysit for more than 5 hours to make more money than Daniel. Option 1 matches the inequality.

User Jgritty
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