the smith family saved $1200 for a summer trip. thier budget is 600 for travel and 100 per day expenses. Write an inequality for the number of days,d,they can be on vacation.

We are given the following details:

- The Smith family has saved $1200 for their trip.
- Their budget for travel is $600.
- Their daily expenses are $100 per day.

Let $ d $ represent the number of days they can stay on vacation. The total cost of their trip will be the sum of the travel budget ($600) and the daily expenses, which is $ 100d $. This total should be less than or equal to their total savings ($1200).

So, the inequality would be:

\[
600 + 100d \leq 1200
\]

### To solve for $ d $:

1. Subtract 600 from both sides:

\[
100d \leq 600
\]

2. Divide both sides by 100:

\[
d \leq 6
\]

Thus, the Smith family can be on vacation for a maximum of 6 days.

Would you like further details or have any questions?

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Here are 5 related questions to consider:
1. How would the inequality change if they saved $1500 instead?
2. What if their daily expenses were $120 per day instead of $100?
3. If they spent $50 more on travel, how many days could they stay?
4. What happens to the inequality if their savings were reduced by $200?
5. If they found a way to reduce their travel cost to $500, how many more days could they stay?

**Tip:** When creating inequalities for budget problems, always include both fixed and variable costs to capture the total expenses.

The Smith family saved $1200 for a summer trip. Their budget is $600 for travel and $100 per day expenses. Write an inequality for the number of days, d, they can be on vacation.

Learn how to create and solve an inequality based on the Smith family's budget for a summer vacation. With $1200 saved, $600 for travel, and $100 per day for expenses, find out how many days they can afford to stay. Suitable for students in Grades 6-8.

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