SOLUTION: a total of 550 people attended a concert. floor tickets cost 2,000 each while balcony tickets cost 1,400 each. if a total of of 1,040,000 was collected. how many of each type of ti

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Question 833187: a total of 550 people attended a concert. floor tickets cost 2,000 each while balcony tickets cost 1,400 each. if a total of of 1,040,000 was collected. how many of each type of ticket were sold?
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
Set f = number of floor tickets
b = number of balcony tickets
2000f + 1400b = 1040000
f + b = 550
solve for b by adding -f to each side
b = 550 -f
substitute (550 - f) for b in 2000f + 1400b = 1040000
2000f + 1400(550 - f) = 1040000
2000f + 770000 - 1400f = 1040000
600f + 770000 = 1040000
add -770000 to each side
600f = 270000
divide each side by 600
f = 450
Since b = 550 - f , b = 100
Let's verify
2000*450 + 1400*100 ?= 1040000
This checks so
f = 450 and b = 100