Question

David has $80 to spend on video games. Used video games cost $10 each, and new video games cost $20 each. Write the equation in standard form that determines the number x of used video games and the number y of new video games he can buy and determine which of the following represents a possible combination of video games

Answer 1

Let's denote the number of used video games as \(x\) and the number of new video games as \(y\). Since used games cost $10 each and new games cost $20 each, the total cost equation can be expressed as:
`P_(initial)`

10x + 20y = 80

This equation represents the constraint on David's budget, ensuring that the total cost of the used and new video games does not exceed his available $80.

Now, let's examine the provided combinations of video games. If we substitute each pair of values for \(x\) and \(y\) into the equation, we can determine if they satisfy the budget constraint. For example, if \(x = 3\) and \(y = 2\), the equation becomes \(10(3) + 20(2) = 30 + 40 = 70\), which is less than $80, making it a valid combination.

In summary, the equation \(10x + 20y = 80\) represents the budget constraint for David's video game purchases. By substituting different values for \(x\) and \(y\), we can determine valid combinations that satisfy the given budget.

**Summary:** The equation \(10x + 20y = 80\) represents David's budget constraint for buying used and new video games. Valid combinations, such as \(x = 3\) and \(y = 2\), can be found by substituting values into the equation.

Answer 2

The standard form of the equation representing the total cost of used (x) and new (y) video games is 10x + 20y - 80 = 0. The correct combination of video games that satisfies the given conditions is (2, 3). Here option B is correct.

Part A:

Let x be the number of used video games and y be the number of new video games. The total cost equation can be expressed as follows:

10x + 20y = 80

Now, let's write it in standard form:

10x + 20y - 80 = 0

So, the equation in standard form is:

10x + 20y - 80 = 0

Part B:

Now, let's check which of the given options represents a possible combination of video games.

A. (0, 4)

10(0) + 20(4) = 0 + 80 = 80 (Incorrect)

B. (2, 3)

10(2) + 20(3) = 20 + 60 = 80 (Correct)

C. (7, 2)

10(7) + 20(2) = 70 + 40 = 110 (Incorrect)

D. (8, 0)

10(8) + 20(0) = 80 + 0 = 80 (Correct)

Therefore, the correct answer is: B. (2, 3)

Complete question:

Dwayne will spend $80 on video games. Used video games cost $10 each, and new video games cost $20 each.

Part A

Write the equation in standard form that determines the number x of used video games and the number y of new video games he can buy.

______x+_______y=_______

Part B

Which of the following represents a possible combination of video games?

A. (0, 4)

B. (2, 3)

C. (7, 2)

D. (8, 0)