Question

3. In order to enter the state fair, there is

an admission cost. Each game is $3.
Steven went to the state fair, played
4 games and spent a total of $20 on
admission and games. Assume the
relationship is linear. Find and interpret
the rate of change and the initial value.​

Answer 1

C = 8 + 3x

The rate of change in the above equation is 3 dollars per game and it interpret the cost per game.

The initial value in the above equation is 8 dollars, which interpret the entry fee that every one person has to pay to enter the fair.

Explanation:

Let the admission cost of the fair is $x and each game is $3.

Now, Steven went to the state fair, played 4 games and spent a total of $20 on admission and games.

So, we can write 20 = x + 4 × 3 {As the relation is linear}

⇒ x = $8

Therefore, the admission cost in the fair is $8.

Therefore, the equation that models the situation is

C = 8 + 3x ............ (1)

Where C is the total cost and x is the number of games played.

So, the rate of change in equation (1) is 3 dollars per game and it interprets the cost per game.

Again, the initial value in equation (1) is 8 dollars, which interprets the entry fee that each person has to pay to enter the fair. (Answer)