Final answer:
Angel charges the greater flat fee of $60 compared to Rose's $50. For a party of 50 guests, Angel would charge $10 more than Rose, with Angel's total being $660 and Rose's total being $650.
Step-by-step explanation:
To determine who charges the greater flat fee between Rose and Angel, we can analyze Angel's charges for a known number of guests and extract the flat fee from that amount. For 10 guests, Angel charges $180. If each guest corresponds to the same fee as in Rose's case, we subtract 10 times that fee from the total charge to find Angel's flat fee:
$180 - (10 guests × $12 per guest) = $180 - $120 = $60
Therefore, Angel's flat fee is $60. Comparing both caterers, Angel charges a greater flat fee than Rose who charges $50.
For part B, to find the difference in total charges for a party of 50 guests between Angel and Rose, we first calculate Rose's total charge:
Rose's charge for 50 guests = $50 flat fee + (50 guests × $12 per guest) = $50 + $600 = $650
We don't have Angel's exact charge for 50 guests, but we can use the flat fee and the per guest charge to determine Angel's charge for any number of guests. Since we know Angel's flat fee ($60) and assume the per guest charge is the same as Rose's ($12), the charge for Angel would be:
Angel's charge for 50 guests = $60 flat fee + (50 guests × $12 per guest) = $60 + $600 = $660
Thus, the difference in total charges for 50 guests would be:
$660 (Angel) - $650 (Rose) = $10
Angel charges $10 more than Rose for a party that includes 50 guests.