Question

Get ready for an amusement park day of fun! You and your family want to spend the day at a theme park. You have pooled your money together and have $685. The tickets to the park are $125 each and there is an online processing fee of $5.75 per ticket. You also need to pay $20 for parking. If you have a family of five, do you have enough money to purchase these tickets? Find an inequality to determine how many tickets can be purchased. Then find how many tickets you are able to purchase based on your inequality.(1 point) Responses 125t+5.75t+20≤685 , and yes, you can purchase the tickets. 125 t plus 5.75 t plus 20 less than or equal to 685 , and yes, you can purchase the tickets. 125t+5.75t≤685 , and yes, you can purchase the tickets. 125 t plus 5.75 t less than or equal to 685 , and yes, you can purchase the tickets. 125t≤685 , and yes, you can purchase the tickets. 125 t less than or equal to 685 , and yes, you can purchase the tickets. 125t+5.75t+20≤685 , and no, you cannot purchase the tickets.

Answer 1

To determine how many tickets you can purchase with your family's budget of $685, we first need to set up the inequality based on the costs involved.

Let $t$ be the number of tickets.

Each ticket costs $125, and there is an online processing fee of $5.75 per ticket. There is also a $20 parking fee.

The total cost for $t$ tickets can be expressed as: $$\text{Total Cost}=125t+5.75t+20$$

This simplifies to: $$\text{Total Cost}=(125+5.75)t+20=130.75t+20$$

Now, we need to set up the inequality: $$130.75t+20\le 685$$

Next, we will solve the inequality for $t$:

1. Subtract 20 from both sides: $$130.75t\le 685-20$$ $$130.75t\le 665$$

2. Divide both sides by 130.75 to solve for $t$: $$t\le \frac{665}{130.75}\approx 5.08$$

Since $t$ must be a whole number (you can't purchase a fraction of a ticket), the maximum number of tickets you can purchase is 5.

Now, let's check if you can afford 5 tickets:

Calculating the total cost for 5 tickets: $$\text{Total Cost for 5 tickets}=130.75\times 5+20=653.75+20=673.75$$

Now compare $673.75 with $685: Since $673.75 is less than $685, you can afford 5 tickets.

So, the correct response includes the inequality and confirms that you can purchase the tickets: $$\text{Answer: }130.75t+20\le 685,\text{ and yes, you can purchase the tickets.}$$

Therefore, the best option from your choices is: "125t + 5.75t + 20 ≤ 685, and yes, you can purchase the tickets."