Write an inequality and solve
A season pass to the amusement park costs $117, and haily admission costs $39. Determine the number of trips to the park for which paying daily admission is three times more expensive than purchasing a season past
Let's assume the number of trips to the park is represented by 'x'.
The cost of purchasing a season pass is $117.
The cost of paying daily admission is $39 * x.
We are asked to find the number of trips for which paying daily admission is three times more expensive than purchasing a season pass.
Mathematically, we can represent this using an inequality:
39x > 117 + 3 * 117
Simplifying the inequality:
39x > 117 + 351
39x > 468
To solve for x, divide both sides of the inequality by 39:
x > 468/39
x > 12
Therefore, the number of trips to the park for which paying daily admission is three times more expensive than purchasing a season pass is greater than 12.
Let's denote the number of trips to the park as "t".
The cost of a season pass is $117.
The cost of daily admission is $39 per trip.
To determine the number of trips for which paying daily admission is three times more expensive than purchasing a season pass, we need to set up an inequality.
Since paying daily admission is three times more expensive than purchasing a season pass, we can write the inequality as:
39t > 3 * 117.
Now we can solve for "t".
Dividing both sides of the inequality by 39, we get:
t > (3 * 117) / 39.
t > 351 / 39.
Simplifying the right side of the inequality, we have:
t > 9.
Therefore, the number of trips should be greater than 9 for paying daily admission to be three times more expensive than purchasing a season pass.
To solve this problem, let's assume the number of trips to the park is represented by the variable 'x'. We can then set up an inequality to represent the given situation.
The cost of daily admission is three times more expensive than purchasing a season pass. This means the cost of daily admission is 3 times the cost of a season pass: 3 * $117 = $351.
The cost of daily admission for 'x' trips would be $39 multiplied by the number of trips, which is 39x.
So, we can set up the inequality as:
39x > 351
Now, to solve for 'x', we need to isolate the variable. Divide both sides of the inequality by 39:
(39x)/39 > 351/39
x > 9
Therefore, the number of trips to the park for which paying daily admission is three times more expensive than purchasing a season pass is any value greater than 9.