A concert hall has 9,000 seats and two s of ticket prices, $22 and $62. Assume t

Question

A concert hall has 9,000 seats and two s of ticket prices, $22 and $62. Assume that all seats in each category can be sold Concert Tickets sold Return required 9,000 9,000 9,000 $511,000 $483,000 $341,000 a. How many tickets of each category should be sold to bring in each of the retuns indicated in the table? $22 Tickets $62 Tickets Concert 1 b. Is it possible to bring in a retun of $108,000 when all the seats are sold? O A. No, $108,000 is greater than the highest possible retum O B. No, $108,000 is less than the smallest possible return. O C. Yes, $108,000 is within the range of possible returns O D. None of the above. Is it possible to bring in a return of $566,000 when all the seats are sold? A. Yes, S566.000 is within the range of possible returns O B. No, $566,000 is less than the smallest possible retun. O c. No, $566,000 is greater than the highest possible return.

Explanation / Answer

(a)

Let the $22 and $62 seats be a and b respectively

Concert 1:

a+b = 9000

22a+62b = 511,000

multiply first equation by 22 and subtract from second

22a+62b-22a-22b = 511,000 - 198,000 = 313,000

40b = 313,000

b = 7825

a = 1175

Concert 1: $22 ticket to be sold are 1175, and $62 ticket to be sold are 7825

Concert 2:

a+b = 9000

22a+62b = 483000

a = 1875, b = 7125

Concert 2: $22 ticket to be sold are 1875, and $62 ticket to be sold are 7125

Concert 3:

a+b = 9000

22a+62b = 341000

a = 5425, b = 3575

Concert 3: $22 ticket to be sold are 5425, and $62 ticket to be sold are 3575

(b).

108,000 is very low so we will have to compare it with the scenario when all the seats are $22

9000 seats for $22, bring in: 22*9000 = 198,000

so it can not go less than 198,000 if all the seats are sold

answer is option B.

(c).

566,000 is very high so we will have to compare it with the scenario when all the seats are $62

9000 seats for $62, bring in: 62*9000 = 558,000

so it can not go more than 558,000 if all the seats are sold

answer is option C.

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