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.
Write your answer in the space below.
2. Write an expression for the amount you would spend on a birthday party at the skating rink.
Write your answer in the space below.
3. How many people could you invite to the bowling alley? Show how you found your answer.
Write your answer in the space below.
4. How many people could you invite to the skating rink? Show your work.
Write your answer in the space below.
5. To which location could you afford to invite more people?
Write your answer in the space below.
Answers
Solution -
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.
Money with me - $50 .
Suppose that I am going to invite an x number of people to the birthday party .
For the bowling alley :
Price per person - $5
Price for rental - $15 .
> 5x + 15 = 50
> 5x = 50 - 15 = 35
> 5x = 35
> x = 7.
For the skating rink :
Price per person : $3
Price for rental : $20 .
> 3x + 20 = 50
> 3x = 50 - 20 = 30
> x = 10 .
I could thus invite 7 people to the bowling alley while I couldn't invite 10 people to the skating rink .
If I wanted to invite as many people as possible , I would choose the skating rink .
______________________________________
Case 1:
Bowling alley:
- Price per person - $5
- Price for rental - $15
5x + 15 = 50
• 5x = 35
• x = 7
Case 2:
Skating rink:
- Price per person : $3
- Price for rental : $20 .
3x + 20 = 50
• 3x = 30
• x = 10
- I will invite 7 people to the bowling alley.
- I can't invite 10 people to the skating rink .
To invite more people, I will choose the skating rink.