A group of friends wants to go to the amusement park. They have no more than $290 to spend on parking and admission. Parking is $11, and tickets cost $23.25 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.
Let x be the number of people who can go to the amusement park.
The cost of parking for x people is 11x.
The cost of admission for x people is 23.25x.
The total cost for parking and admission for x people is 11x + 23.25x = 34.25x.
Since they have no more than $290 to spend, the inequality is:
34.25x ≤ 290
To solve the inequality, divide both sides by 34.25:
x ≤ 290/34.25
x ≤ 8.465
Since the number of people must be a whole number, the maximum number of people who can go to the amusement park is 8. Answer: \boxed{8}.
A shipping container will be used to transport several 120-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 14300 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine
x, the number of 120-kilogram crates that can be loaded into the shipping container.
Answer
Let x be the number of 120-kilogram crates that can be loaded into the shipping container.
The weight of x crates is 120x kilograms.
The total weight of the shipment, including the already loaded crates, is 120x + 14300 kilograms.
Since the greatest weight that can be loaded into the container is 27500 kilograms, the inequality is:
120x + 14300 ≤ 27500
To solve the inequality, subtract 14300 from both sides:
120x ≤ 13200
Divide both sides by 120:
x ≤ 110
Therefore, the maximum number of 120-kilogram crates that can be loaded into the shipping container is 110. Answer: \boxed{110}.
Let x be the number of people who can go to the amusement park.
The cost of parking for x people is given by: 11x
The cost of tickets for x people is given by: 23.25x
The total cost should not exceed $290, so we can write the inequality:
11x + 23.25x ≤ 290
Combining like terms, we get:
34.25x ≤ 290
Now, we can solve for x:
x ≤ 290 / 34.25
x ≤ 8.467836257
Since we cannot have a fraction of a person, we can round down to the nearest whole number, which means:
x ≤ 8
Therefore, the maximum number of people who can go to the amusement park is 8.