How many of each type of ticket should he buy?

Question

Scott is in charge of purchasing a variety of tickets to a baseball game to be given to employees who met or exceeded their sales quotas for the past month. There are 3 types of tickets available for the game at a cost of $25 apiece, $35 apiece, or $50 apiece. Scott needs to buy 40 tickets in all and can spend $1670. He wants to buy twice as many $35 tickets as $25 tickets. How many of each type of ticket should he buy?

Answer 1

A=# of $25 tickets

B=# of $35 tickets

C=# of $50 tickets

A+B+C=40 but he wants to buy twice as many $35(B) tickets as $25(A) tickets

A+2A+C=40

3A+C=40

$25A+$35(2A)+$50C=$1670

$25A+$70A+$50C=$1670

$95A+$50C=$1670

3A+C=40 so C=40-3A

substitute

$95A+$50(40-3A)=$1670

95A+2000-150A=1670

-55A+2000=1670

-55A=1670-2000

-55A=-330

55A=330

A=330/55

A=6 $25 tickets

B=12 $35 tickets

40-6-12=40-18=22

C=22 $50 tickets

check: 6*$25+12*$35+22*$50=$150+$420+$1100=$1670