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?

see below

Step-by-step explanation:

Bowling:

15+5x  where x is the number of people

Skating:

20+3x

We have 50 dollars so the amount must be less than or equal to 50

Bowling

15+5x≤50

Subtract 15 from each side

15-15+5x≤50-15

5x ≤35

Divide each side by 5

5x/5 ≤35/5

x ≤7

She can have 7 or less people

Skating

We have 50 dollars so the amount must be less than or equal to 50

20+3x  ≤50

Subtract 20 from each side

20-20+3x  ≤50-20

3x  ≤30

Divide each side by 3

3x/3 ≤30/3

x ≤10

She can have up to 10 people

She can invite more people skating

1) C = 15 + 5x

2) C = 20 + 3x

3) 7

4) 10

5) Skating rink

Step-by-step explanation:

C : cost

Fixed: 15

Additional: 5

For x people,

C = 15 + 5x

Budget is 50:

15 + 5x《50

3x《35

x《7

C : cost

Fixed: 20

Additional: 3

For x people,

C = 20 + 3x

Budget is 50

20 + 3x《50

3x《30

x《10

Since 10 > 7, she can invite more people at the skating rink

were is the equation