the town librarian bought a combination of new - release movies on dvd for $20 and classic movies on dvd for…

the town librarian bought a combination of new - release movies on dvd for $20 and classic movies on dvd for $8. let x represent the number of new releases, and let y represent the number of classics. if the librarian had a budget of $500 and wanted to purchase as many dvds as possible, which values of x and y could represent the number of new - release and classic movies bought?\no x = 8, y = 45\no x = 10, y = 22\no x = 16, y = 22\no x = 18, y = 18

the town librarian bought a combination of new - release movies on dvd for $20 and classic movies on dvd for $8. let x represent the number of new releases, and let y represent the number of classics. if the librarian had a budget of $500 and wanted to purchase as many dvds as possible, which values of x and y could represent the number of new - release and classic movies bought?\no x = 8, y = 45\no x = 10, y = 22\no x = 16, y = 22\no x = 18, y = 18

Answer

Explanation:

Step1: Set up cost - equation

The cost of new - release movies is $20x$ and the cost of classic movies is $8y$, and the budget is $500$. So the equation is $20x + 8y\leq500$. Also, we want to maximize $N=x + y$.

Step2: Check option A

For $x = 8$ and $y = 45$: The cost is $20\times8+8\times45=160 + 360=520>500$. So this option is not valid.

Step3: Check option B

For $x = 10$ and $y = 22$: The cost is $20\times10+8\times22=200 + 176 = 376$. The number of DVDs is $N=10 + 22=32$.

Step4: Check option C

For $x = 16$ and $y = 22$: The cost is $20\times16+8\times22=320+176 = 496$. The number of DVDs is $N=16 + 22=38$.

Step5: Check option D

For $x = 18$ and $y = 18$: The cost is $20\times18+8\times18=360 + 144=504>500$. So this option is not valid.

Answer:

C. $x = 16,y = 22$