Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Select the correct answer.

Helena has saved [tex]\$595[/tex] to put toward snowboarding equipment and lift tickets at the hill. Each lift ticket costs [tex]\$35[/tex]. If she wants to have more than [tex]\$420[/tex] of her savings left to spend on equipment, which inequality represents the number of lift tickets she can buy?

A. [tex]x \ \textless \ 5[/tex]
B. [tex]x \leq 4[/tex]
C. [tex]x \ \textgreater \ 7[/tex]
D. [tex]x \geq 7[/tex]


Sagot :

To determine the correct inequality expressing the number of lift tickets Helena can buy, let's go through the situation step-by-step.

1. Total Savings and Ticket Costs:
- Helena has [tex]$595 saved. - Each lift ticket costs $[/tex]35.

2. Savings Requirement:
- Helena wants to have more than [tex]$420 left for equipment. 3. Calculation of Remaining Savings: - If Helena buys \( x \) lift tickets, the cost is \( 35x \). - The remaining savings after buying \( x \) lift tickets would be \( 595 - 35x \). 4. Formulating the Inequality: - We need Helena's remaining savings to be more than $[/tex]420, so:
[tex]\[ 595 - 35x > 420 \][/tex]

5. Solve for [tex]\( x \)[/tex]:
- Subtract 420 from both sides of the inequality:
[tex]\[ 595 - 35x - 420 > 0 \][/tex]
Simplifying the left-hand side, we get:
[tex]\[ 175 - 35x > 0 \][/tex]
- Subtract 175 from both sides:
[tex]\[ 175 - 175 - 35x > 0 - 175 \][/tex]
Simplifying, we get:
[tex]\[ -35x > -175 \][/tex]
- Divide both sides by -35, and remember to reverse the inequality sign when dividing by a negative number:
[tex]\[ x < \frac{175}{35} \][/tex]

Simplifying:
[tex]\[ x < 5 \][/tex]

6. Interpreting the Result:
- This implies that the maximum number of tickets she can buy is 4 because for [tex]\( x < 5 \)[/tex], the integer solutions are [tex]\( x = 0, 1, 2, 3, 4 \)[/tex].

7. Choosing the Correct Inequality:
- Among the given options:
- A. [tex]\( x < 5 \)[/tex]
- B. [tex]\( x \leq 4 \)[/tex]
- C. [tex]\( x > 7 \)[/tex]
- D. [tex]\( x \geq 7 \)[/tex]

- The correct inequality that aligns with our solution is:
[tex]\( x \leq 4 \)[/tex].

Thus, the correct answer is:
[tex]\[ \boxed{B} \, x \leq 4 \][/tex]
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.