Question

Yasmani uses a gift card to buy video games. The initial value of the gift card is $250 and each game costs $15. V(x)
represents the amount of money, V
, in dollars that is still left on the gift card after purchasing, x
, games. (1 point)
Part A: The function is V(x) =



Part B: Graph the function. (Link to Desmos)

Part C: The constraints are:
and

Part D: For every game bought, the value of the gift card
by $

Part E: Find the solution of V(x) = 70

x=

Answer 1

Let's break down the problem step by step.

### Part A: The function

The initial value of the gift card is $250, and each game costs $15. If Yasmani buys \( x \) games, the total amount spent on games is \( 15x \). Therefore, the amount of money left on the gift card can be represented by the function:

\[ V(x) = 250 - 15x \]

### Part B: Graph the function

To graph the function \( V(x) = 250 - 15x \), you would typically use graphing software like Desmos. The function is a linear equation with a y-intercept at 250 and a slope of -15. The graph will be a straight line descending from 250.

### Part C: The constraints

The constraints here would be based on the scenario that Yasmani can only buy a non-negative number of games, and also can’t exceed the total value of the gift card.

1. \( x \geq 0 \) (Yasmani cannot buy a negative number of games)
2. \( V(x) \geq 0 \) (The amount left on the gift card cannot be negative)

To determine the upper limit for \( x \):
\[ 250 - 15x \geq 0 \]
\[ 250 \geq 15x \]
\[ \frac{250}{15} \geq x \]
\[ x \leq 16.\overline{6} \]

Since \( x \) must be a whole number, the maximum number of games Yasmani can buy is 16. So the complete constraints are:

- \( 0 \leq x \leq 16 \)

### Part D: For every game bought, the value of the gift card decreases by

Each game costs $15, therefore for every game bought, the value of the gift card decreases by:

\[
15 \text{ dollars}
\]

### Part E: Find the solution of \( V(x) = 70 \)

We need to solve for \( x \) in the equation:

\[
V(x) = 70
\]

Substituting in the function:

\[
250 - 15x = 70
\]

Now, solve for \( x \):

1. Subtract 250 from both sides:
\[
-15x = 70 - 250 \implies -15x = -180
\]

2. Divide by -15:
\[
x = \frac{-180}{-15} = 12
\]

Therefore, the solution is:

\[
x = 12
\]

### Summary of Answers
- **Part A:** \( V(x) = 250 - 15x \)
- **Part C:** \( 0 \leq x \leq 16 \)
- **Part D:** The value of the gift card decreases by $15 for every game bought.
- **Part E:** \( x = 12 \)