Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To solve the exercise you can propose the following system of linear equations:
[tex]\begin{gathered} x+y=23\Rightarrow\text{ Equation 1} \\ 32x+26y=688\text{ }\Rightarrow\text{ Equation 2} \\ \text{ Where} \\ x\text{ is the number of double rooms and} \\ y\text{ is the number of single rooms} \end{gathered}[/tex]To solve the system of linear equations you can use the method of reduction or elimination. To do this first multiply Equation 1 by -32 and add both equations, then solve for the variable y:
[tex]\begin{gathered} (x+y)\cdot-32=23\cdot-32 \\ -32x-32y=-736 \\ \text{ Now add both equations} \\ -32x-32y=-736 \\ 32x+26y=688\text{ +} \\ ------------- \\ 0x-6y=-48 \\ -6y=-48 \\ \text{ Divide by -6 from both sides of the equation} \\ \frac{-6y}{-6}=\frac{-48}{-6} \\ y=8 \end{gathered}[/tex]Finally, replace the value of the variable y into any of the initial equations and solve for the variable x. For example, replace the value of the variable y in Equation 1:
[tex]\begin{gathered} x+y=23 \\ x+8=23 \\ \text{ Subtract 8 from both sides of the equation} \\ x+8-8=23-8 \\ x=15 \end{gathered}[/tex]Therefore, 15 double rooms and 8 single rooms were rented.
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.