Question

1. at a campground, kayak rental company a charges a fixed amount of $10 plus $8 per hour for renting a one - person kayak. company b charges a fixed amount of $6 plus $10 per hour for a one - person kayak. select all of the statements that are true. for 1 hour, both companies charge the same amount. for 1 hour, company a charges more than company b. for 2 hours, both companies charge the same amount. for 3 hours, company a charges more than company b. for 4 hours, company b charges more than company a. 65) an inequality is shown. $8x - 30leq5x + 3$ which graph represents the solution to the inequality?

Explanation:

Question 64

Step1: Define the cost functions

Let \( h \) be the number of hours. The cost for Company A, \( C_A \), is \( C_A = 10 + 8h \). The cost for Company B, \( C_B \), is \( C_B = 6 + 10h \).

Step2: Evaluate for 1 hour

For \( h = 1 \):
\( C_A = 10 + 8(1) = 18 \)
\( C_B = 6 + 10(1) = 16 \)
So, Company A charges more than Company B for 1 hour.

Step3: Evaluate for 2 hours

For \( h = 2 \):
\( C_A = 10 + 8(2) = 26 \)
\( C_B = 6 + 10(2) = 26 \)
Both companies charge the same for 2 hours.

Step4: Evaluate for 3 hours

For \( h = 3 \):
\( C_A = 10 + 8(3) = 34 \)
\( C_B = 6 + 10(3) = 36 \)
Company B charges more than Company A for 3 hours.

Step5: Evaluate for 4 hours

For \( h = 4 \):
\( C_A = 10 + 8(4) = 42 \)
\( C_B = 6 + 10(4) = 46 \)
Company B charges more than Company A for 4 hours.

Step1: Solve the inequality \( 8x - 30 \leq 5x + 3 \)

Subtract \( 5x \) from both sides:
\( 8x - 5x - 30 \leq 3 \)
\( 3x - 30 \leq 3 \)

Step2: Add 30 to both sides

\( 3x \leq 3 + 30 \)
\( 3x \leq 33 \)

Step3: Divide both sides by 3

\( x \leq \frac{33}{3} \)
\( x \leq 11 \)

The solution is all real numbers less than or equal to 11. The graph should have a closed circle at 11 and an arrow pointing to the left.

Answer:

• For 1 hour, company A charges more than company B.
• For 2 hours, both companies charge the same amount.
• For 4 hours, company B charges more than company A.

Question 65