Question

charlie and susan are planning a party for 10 people. charlie finds a location that charges an initial fee of $20 plus $25 per person. susan finds a location whose rental fee is represented by the equation ( y = 15x + 100 ), where ( x ) is the number of people in attendance and ( y ) is the total cost. select all the statements that are true. - charlies location is a cheaper location. - susans location is cheaper for 10 people. - the charge for each additional person is greater for susans location. - the charge for each additional person is greater for charlies location. - if the number of people at the party changes to 12, the total cost at each location is the same.

Explanation:

Step1: Calculate Charlie's 10-person cost

Total cost = Initial fee + (Cost per person × Number of people)
$\text{Cost}_{\text{Charlie (10)}} = 20 + (25 \times 10) = 20 + 250 = 270$

Step2: Calculate Susan's 10-person cost

Substitute $x=10$ into $y=15x+100$
$\text{Cost}_{\text{Susan (10)}} = 15(10) + 100 = 150 + 100 = 250$

Step3: Compare per-person additional cost

Charlie's per-person rate = $\$25$, Susan's per-person rate = $\$15$

Step4: Calculate cost for 12 people

Charlie: $\text{Cost}_{\text{Charlie (12)}} = 20 + (25 \times 12) = 20 + 300 = 320$
Susan: $\text{Cost}_{\text{Susan (12)}} = 15(12) + 100 = 180 + 100 = 280$

Answer:

• Susan's location is cheaper for 10 people
• The charge for each additional person is greater for Charlie's location