Mathematics, 05.10.2019 16:00 zurfluhe

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? x = 8, y = 45 x = 10, y = 22 x = 16, y = 22 x = 18, y = 18

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Answer from: dumbdumbkylee

x = 16, y = 22.

Further explanation

We will solve the problem of linear programming. The case is simple, but we must still be accurate in doing so.

Given:

The cost for new-release movies on DVD for $20 and classic movies on DVD for $8. The librarian had a budget of $500 and wanted to purchase as many DVDs as possible.Let x represent the number of new releases and let y represent the number of classics.

Question:

Which values of x and y could represent the number of new-release and classic movies bought?

The Process:

Because the number of goods must be positive, then

$\boxed{ \ x \geq 0 \ }$ $\boxed{ \ y \geq 0 \ }$

The total number of DVDs purchased is 20x + 8y (in USD) and must not exceed $500. Thus, we have the inequality

$\boxed{ \ 20x + 8y \leq 500 \ }$

Let's examine one by one for each available option, whether it meets the inequality above.

Option A

$\boxed{ \ x = 8, y = 45 \ } \rightarrow \boxed{ \ 20(8) + 8(45) = 520 \ }$

This did not meet and was rejected.

Option B

$\boxed{ \ x = 10, y = 22 \ } \rightarrow \boxed{ \ 20(10) + 8(22) = 376 \ }$

It fulfills but then we will examine it again.

Option C

$\boxed{ \ x = 16, y = 22 \ } \rightarrow \boxed{ \ 20(16) + 8(22) = 496 \ }$

It fulfills but then we will examine it again.

Option D

$\boxed{ \ x = 18, y = 18 \ } \rightarrow \boxed{ \ 20(18) + 8(18) = 504 \ }$

This did not meet and was rejected.

Comparison of Option B and Option C

$\boxed{ \ x = 10, y = 22 \ } \rightarrow \boxed{ \ x + y = 10 + 22 = 32 \ DVDs \ }$ $\boxed{ \ x = 16, y = 22 \ } \rightarrow \boxed{ \ x + y = 16 + 22 = 38 \ DVDs \ },$ this means more DVDs.

The librarian wanted to purchase as many DVDs as possible. Thus, values of x and y could represent the number of new-release and classic movies bought is $\boxed{ \ x = 16, y = 22 \ }$ .

Learn moreWhich expression represents the amount of change Huang should receive? Anna has the most money Does Marcus pay tax?

Keywords: linear programming, the town librarian, a combination of new-release movies on DVD, classic, purchases, budget, as many DVDs as possible

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

Answer from: Quest

6,250

step-by-step explanation:

to get the area, multiply 360 by 160.(57,600)

to find out how many bags of fertilizer it will take, first figure out how many square feet one bag can hold. divide 1000 by 8(125) to get the unit rate(how many square feet one pound of fertilizer can hold)and multiply it by 50(6250). if i haven't made a mistake, that is the answer.

Answer from: Quest

i dont know

step-by-step explanation:

umm. i dont know

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