SOLUTION: I have a couple of questions.They are word problems dealing with planning for a dance and keeping the ticket price low. 1. Band A charges $600 to play for the evening. Band B c

Question 138128: I have a couple of questions.They are word problems dealing with planning for a dance and keeping the ticket price low.
1. Band A charges $600 to play for the evening. Band B charges $350 plus $1.25 for each ticket sold. Write a linear equation for the cost of each band. Also find the number of tickets for which the cost of the two bands will be equal.
2. A caterer charges a fixed cost for preparing dinner plus a cost for each person served. You know that the cost for 100 people will be$750 and the cost for 150 people will be $ 1050. Find the caterer's fixed cost and the cost per person served.
3.From the information above , assume that 200 people will come to the dance. Which band would you choose and the cost per ticket that you need to charge to cover expenses?
Please, please HELP!!!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1. Band A charges $600 to play for the evening. Band B charges $350 plus $1.25 for each ticket sold. Write a linear equation for the cost of each band. Also find the number of tickets for which the cost of the two bands will be equal.
Let x = number of tickets that will make the band costs equal.
:
Band B cost = Band A cost
1.25x + 350 = 600
1.25x = 600 - 350; subtracted 350 from both sides
1.25x = 250
x = ; divided both sides by 1.25
x = 200 Tickets
:
Check solution: 1.25(200) + 350 = 600
:
:
2. A caterer charges a fixed cost for preparing dinner plus a cost for each person served. You know that the cost for 100 people will be$750 and the cost for 150 people will be $ 1050. Find the caterer's fixed cost and the cost per person served.
:
Let x = per person cost
Let y = fixed cost
;
Write an equation for each situation
150x + y = 1050
100x + y = 750
------------------Subtracting eliminates y, find x
50x + 0y = 300
x =
x = $6 per person
:
Find y:
100(6) + y = 750
y = 750 - 600
y = $150 is the fixed cost.
:
:
3.From the information above , assume that 200 people will come to the dance. Which band would you choose and the cost per ticket that you need to charge to cover expenses?
:
Check the cost using band A and 200 people, including food
600 + 150 + (6*200) =
600 + 150 + 1200 = $1950
Cost per ticket: = 1950/200 = $9.75
:
Cost using band B, 200 people, including food:
350 + 1.25(200) + 150 + (6*200) =
350 + 250 + 150 + 1200 = $1950
Cost per ticket: 1950/200 = $9.75
:
It would cost the same
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