A group of friends wants to go to the amusement park. They have no more than $160 to spend on parking and admission. Parking is $10.50, and tickets cost $32.50 per person, including tax. Write and solve an inequality which can be used to determine
x, the number of people who can go to the amusement park.
Answer
32.50x + 10.50 ≤ 160
Subtract 10.50 from both sides:
32.50x ≤ 149.50
Divide both sides by 32.50:
x ≤ 4.6
Therefore, the number of people who can go to the amusement park is 4 or less.
To determine the number of people who can go to the amusement park, we can use the following inequality:
$10.50 + $32.50x ≤ $160
This inequality represents the total cost of parking ($10.50) added to the cost of admission ($32.50) multiplied by the number of people (x). This sum should be less than or equal to the total budget of $160.
To solve this inequality for x, we can rearrange it as follows:
$32.50x ≤ $160 - $10.50
$32.50x ≤ $149.50
Now, we can isolate x by dividing both sides by $32.50:
x ≤ $149.50 / $32.50
x ≤ 4.6
Since the number of people must be a whole number, the group of friends can invite a maximum of 4 people (x ≤ 4) to the amusement park while staying within their budget.