Login
Premium
Home Question Bank Math Algebra
Question
upstudy study bank question image url

8. KAYAK The cost \( y \) (in dollars) to rent a kayak is proportional to the number \( x \) of hours that you rent the kayak. It costs \( \$ 27 \) to rent the kayak for 3 hours. a. Write an equation that represents the situation. b. Interpret the slope. c. How much does it cost to rent the kayak for 5 hours?

Ask by Weber Phillips. in the United States
Jan 21,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

a. The equation is \( y = 9x \). b. The slope \( 9 \) means it costs \$9 per hour to rent the kayak. c. Renting for 5 hours costs \$45.

Solution

Let's solve each part of the problem step by step. ### **a. Write an equation that represents the situation.** Since the cost \( y \) is **proportional** to the number of hours \( x \), we can express this relationship with the equation: \[ y = kx \] where: - \( y \) is the total cost in dollars, - \( x \) is the number of hours, - \( k \) is the **constant of proportionality** (i.e., the cost per hour). **Given:** It costs \$27 to rent the kayak for 3 hours. We can substitute these values into the equation to find \( k \): \[ 27 = k \times 3 \] Solving for \( k \): \[ k = \frac{27}{3} = 9 \] **Therefore, the equation representing the situation is:** \[ y = 9x \] ### **b. Interpret the slope.** In the equation \( y = 9x \): - The **slope** is **9**. - **Interpretation:** The slope represents the **cost per hour** to rent the kayak. Specifically, it costs **\$9 per hour** to rent the kayak. ### **c. How much does it cost to rent the kayak for 5 hours?** To find the cost \( y \) for 5 hours (\( x = 5 \)), substitute \( x = 5 \) into the equation: \[ y = 9x = 9 \times 5 = 45 \] **Therefore, it costs \$45 to rent the kayak for 5 hours.** --- **Summary:** a. The equation is \( y = 9x \). b. The slope \( 9 \) represents the cost of \$9 per hour to rent the kayak. c. Renting the kayak for 5 hours costs \$45.

Reviewed and approved by the UpStudy tutoring team

error msg
Explain
Simplify this solution

Bonus Knowledge

To begin, we can establish that the cost \( y \) is proportional to the number of hours \( x \), which allows us to express this relationship with the equation: \[ y = kx \] To find the constant \( k \), we can use the information provided: It costs \( 27 \) dollars for \( 3 \) hours. Thus, \( k = \frac{y}{x} = \frac{27}{3} = 9 \). This gives us the final equation: \[ y = 9x \] The slope \( k \) represents the cost per hour to rent the kayak. In this case, the slope is \( 9 \), meaning it costs \( 9 \) dollars for each hour you rent the kayak. This is a straightforward way to visualize how cost increases with time. To find the cost to rent the kayak for \( 5 \) hours, we simply apply our equation: \[ y = 9 \times 5 = 45 \] Therefore, renting the kayak for \( 5 \) hours will cost you \( 45 \) dollars.

Related Questions

2) \( a^{2}-11 a-12 \)
Algebra South Africa Jan 22, 2025
4. \( \frac{2 x-1}{3}-\frac{4 x-8}{6} \) 6. \( \frac{3}{x-1}+\frac{1}{1-x} \) 8. \( \frac{x}{x+y}+\frac{y}{x-y} \) 10. \( \frac{x+3}{x-3}-\frac{x-3}{x+3} \) 12. \( \frac{5}{3(a-b)}+\frac{3}{2(b-a)} \) 14. \( \frac{x}{x^{2}-y^{2}}+\frac{y}{y^{2}-x^{2}} \) 16. \( \frac{4 x}{(x+y)^{2}}-\frac{4}{x+y} \) 18. \( \frac{3 a}{9 a^{2}-4 b^{2}}-\frac{1}{3 a+2 b} \) 20. \( \frac{2 y}{(x-2 y)^{2}}+\frac{1}{x-2 y} \)
Algebra United States Jan 22, 2025
1. Find the products. \( \begin{array}{ll}\text { a) }(x+2)(x+3) & \text { (b) }(p-3)(p-4) \\ \text { c) }(a-2)(a+3) & \text { d) }(2 x-3)(3 x+1) \\ \text { e) }(2 y+5)(3 y-2) & \text { f) }(3 a-7)(2 a+1) \\ \text { g) }(2 a-3)(3 a-2) & \text { (h) }(4 y+1)(7 y-2) \\ \text { i) }(x-3)(x-2) & \text { j) }(4 a-2)(3 a+5) \\ \text { k) }(2 x-3 y)(2 x+4 y) & \text { 1) }(2 a-7 b)(3 a-2 b) \\ \text { m) }(7 x+3 y)(2 x-4 y) & \text { n) }(3 a-2 b)(2 a+11 b)\end{array} \)
Algebra South Africa Jan 22, 2025
2. Find the products. \( \begin{array}{ll}\text { a) }(x+1)(x+3) & \text { b) }(a+3)(a+4) \\ \text { c) }\left(x^{2}-1\right)\left(2 x^{2}+3\right) & \text { d) }\left(a^{2}-2\right)\left(a^{2}+2\right) \\ \text { e) }(3 x y+2 z)(2 x y-3 z) & \text { f) }(p r+2 t)(3 p r-t) \\ \text { g) }\left(x^{2}-4\right)\left(4 x^{2}-3\right) & \text { h) }\left(2 a^{2}+1\right)\left(3 a^{2}+1\right) \\ \text { i) }\left(x+\frac{1}{2}\right)\left(x+\frac{1}{4}\right) & \text { j) }\left(2 x+\frac{1}{3}\right)\left(3 x-\frac{1}{2}\right) \\ \text { k) }(2 a-b)(2 a+b) & \text { l) }(3 x+2 y)(3 x-2 y) \\ \text { m) }\left(\frac{1}{2} x+\frac{1}{3} y\right)\left(\frac{1}{3} x-\frac{1}{2} y\right) & \text {-n) }(x+3)^{2}\end{array} \)
Algebra South Africa Jan 22, 2025
\begin{tabular}{l} (a) Simplify \( \frac{2}{y^{0}} \) \\ (b) Simplify fully \( \left(16 a^{4}\right)^{\frac{3}{4}} \) \\ 5 \\ Factorise fully \( 18 c^{3} d^{2}-21 c^{2} \) \\ (Total for Question 4 is 3 marks) \\ \hline\end{tabular}
Algebra United Arab Emirates Jan 22, 2025

Latest Algebra Questions

2. Find the products. \( \begin{array}{ll}\text { a) }(x+1)(x+3) & \text { b) }(a+3)(a+4) \\ \text { c) }\left(x^{2}-1\right)\left(2 x^{2}+3\right) & \text { d) }\left(a^{2}-2\right)\left(a^{2}+2\right) \\ \text { e) }(3 x y+2 z)(2 x y-3 z) & \text { f) }(p r+2 t)(3 p r-t) \\ \text { g) }\left(x^{2}-4\right)\left(4 x^{2}-3\right) & \text { h) }\left(2 a^{2}+1\right)\left(3 a^{2}+1\right) \\ \text { i) }\left(x+\frac{1}{2}\right)\left(x+\frac{1}{4}\right) & \text { j) }\left(2 x+\frac{1}{3}\right)\left(3 x-\frac{1}{2}\right) \\ \text { k) }(2 a-b)(2 a+b) & \text { l) }(3 x+2 y)(3 x-2 y) \\ \text { m) }\left(\frac{1}{2} x+\frac{1}{3} y\right)\left(\frac{1}{3} x-\frac{1}{2} y\right) & \text {-n) }(x+3)^{2}\end{array} \)
Algebra South Africa Jan 22, 2025
5. \( \begin{aligned} j-9 \pi= & 12 \pi \\ +9 \pi & +9 \pi\end{aligned} \)
Algebra United States Jan 22, 2025
7 Expand and simplify \( 5 x(3 x+4)(2 x-1) \)
Algebra United Arab Emirates Jan 22, 2025
1. Find the products. \( \begin{array}{ll}\text { a) }(x+2)(x+3) & \text { (b) }(p-3)(p-4) \\ \text { c) }(a-2)(a+3) & \text { d) }(2 x-3)(3 x+1) \\ \text { e) }(2 y+5)(3 y-2) & \text { f) }(3 a-7)(2 a+1) \\ \text { g) }(2 a-3)(3 a-2) & \text { (h) }(4 y+1)(7 y-2) \\ \text { i) }(x-3)(x-2) & \text { j) }(4 a-2)(3 a+5) \\ \text { k) }(2 x-3 y)(2 x+4 y) & \text { 1) }(2 a-7 b)(3 a-2 b) \\ \text { m) }(7 x+3 y)(2 x-4 y) & \text { n) }(3 a-2 b)(2 a+11 b)\end{array} \)
Algebra South Africa Jan 22, 2025
1. Find the products. \( \begin{array}{ll}\text { a) }(x+2)(x+3) & \text { \b) }(p-3)(p-4) \\ \text { c) }(a-2)(a+3) & \text { d) }(2 x-3)(3 x+1) \\ \text { e) }(2 y+5)(3 y-2) & \text { f) }(3 a-7)(2 a+1) \\ \text { g) }(2 a-3)(3 a-2) & \text { (h) }(4 y+1)(7 y-2) \\ \text { i) }(x-3)(x-2) & \text { j) }(4 a-2)(3 a+5) \\ \text { k) }(2 x-3 y)(2 x+4 y) & \text { \l) }(2 a-7 b)(3 a-2 b) \\ \text { m) }(7 x+3 y)(2 x-4 y) & \text { n) }(3 a-2 b)(2 a+11 b) \\ \text { 2. Find the products. } & \text { b) }(a+3)(a+4) \\ \text { a) }(x+1)(x+3) & \text { (d) }\left(a^{2}-2\right)\left(a^{2}+2\right) \\ \text { c) }\left(x^{2}-1\right)\left(2 x^{2}+3\right) & \text { f) }(p r+2 t)(3 p r-t) \\ \text { (e) }(3 x y+2 z)(2 x y-3 z) & \text { h) }\left(2 a^{2}+1\right)\left(3 a^{2}+1\right) \\ \text { g) }\left(x^{2}-4\right)\left(4 x^{2}-3\right) & \text { j) }\left(2 x+\frac{1}{3}\right)\left(3 x-\frac{1}{2}\right) \\ \text { i) }\left(x+\frac{1}{2}\right)\left(x+\frac{1}{4}\right) & \text { l) }(3 x+2 y)(3 x-2 y) \\ \text { k) }(2 a-b)(2 a+b) & \text { n) }(x+3)^{2} \\ \text { m) }\left(\frac{1}{2} x+\frac{1}{3} y\right)\left(\frac{1}{3} x-\frac{1}{2} y\right) & \end{array} \)
Algebra South Africa Jan 22, 2025
Prev Next
Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy