Question 138128
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.
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Band B cost = Band A cost
1.25x + 350 = 600
1.25x = 600 - 350; subtracted 350 from both sides
1.25x = 250
x = {{{250/1.25}}}; divided both sides by 1.25
x = 200 Tickets
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Check solution: 1.25(200) + 350 = 600
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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.
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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 = {{{300/50}}}
x = $6 per person
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Find y: 
100(6) + y = 750
y = 750 - 600
y = $150 is the fixed cost.
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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?
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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 
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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
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It would cost the same