Question

A bowling alley and a skating rink both offer birthday party rentals. The bowling alley costs $5 per person plus a $15 room rental fee. The skating rink costs $3 per person plus a $20 room rental fee. You have $50. If you want to invite as many people as possible, which location should you choose? Follow the steps to decide on the party location.
1. Write an expression for the amount you would spend on a birthday party at the bowling alley. Let x represent the number of people you invite.

2. Write an expression for the amount you would spend on a birthday party at the skating rink.

3. How many people could you invite to the bowling alley? Show how you found your answer.

4. How many people could you invite to the skating rink? Show your work.

5. To which location could you afford to invite more people?

Answer 1

Answer:

1. (50-15) - 5x

2. (50-20) - 3x

3. 50 - 15 = 35   35/5 = 7 people

4. 50 - 20 = 30  30/3 = 10 people

5. The skating rink

Step-by-step explanation:

1. The 50-15 at the beginning shows the cost of the room being subtracted from your funds and then subtracting 5x shows that the cost of all the people is the cost per person times the amount of people.

2. The 50-20 at the beginning shows the cost of the room being subtracted from your funds and then subtracting 3x shows that the cost of all the people is the cost per person times the amount of people.

Answer 2

Answer:

1. 50 = 5x+15

2. 50 = 3x+20

3. 7

4. 10

5. Skating Rink

Step-by-step explanation:

1. As the maximum amount of money is 50 dollars, you are given that there is a 5 dollar entry *per* person, alongside the 15 room rental fee added on. That is where the equation 5x+15 = 50 comes from

2. The same can be said with the skating rink, with different numbers. 3 *per* person plus the extra 20 room rental fee.

3. 50 = 5x+15 can be solved by subtracting 15 by both sides. This gives us 35=5x and dividing by 5 will give us 7 = x

4. 50 = 3x+20 can be solved by subtracting 20 by both sides. This gives us 30=3x and dividing by 3 will give us 10 = x

5. As 10>7, it's apparent that you can bring more people to the Skating Rink