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LiberT
07-17-2007, 04:11 PM
Adult tickets for a play cost \$13 and child tickets cost \$6. If there were 22 people at a performance and the theater collected \$167 from ticket sales, how many adults and how many children attended the play? Show the equations used.

Vince
07-17-2007, 04:52 PM
So let x be the number of adults. Then 22-x is the number of children.The equation for the sales is:S = 13*x + 6*(22-x) = 167 7x + 132 = 167 7x = 35 x = 5Therefore 5 adults and 17 children attended.

MathProf
07-17-2007, 04:57 PM
Systems of Linear Equations:Set up your variables: (unknowns)Let A = Number of adult tickets soldLet C = Number of child's tickets soldThe first equation is all about the number of tickets sold:A + C = 22The second equation is all about money :)13A + 6C = 167Use substitution: C = 22 - A13A + 6(22-A) = 16713A + 132 - 6A = 1677A = 35A = 5C = 22 - A = 22 - 5 = 17Check: 5 + 17 = 22 yep!13(5) + 6 (17) = 65 + 102 = 167 yep!

Gary H
07-17-2007, 05:26 PM
There were 22 people total, right? So let's say that the number of adults was x. Then the number of children must have been 22-x, right? And the number of adults times \$13 plus the number of children times \$6 must equal \$167. So you have an equation -\$13x + \$6(22-x) = \$167 ==\$13x +\$132 - \$6x = \$167 ==\$7x + \$132 = \$167 ==\$7x = \$35 ==x = \$35/\$7 = 5 = number of adults, and the number of children's ticket sold was 22-x = 22-5 = 17

team
07-17-2007, 09:11 PM
its a guess and test thing..use : 13x + 6y= 167since 167 is an odd number (not really divisible by anything), you know you need an odd # of adult tickets (for example: 1*13 or 3*13 or 5*13) these will give an odd number. subtract 1*13 or 3*13 or 5*13..ect... from 167 (now you have an even number)and see if that number is divisible by 6.. if it is, then you have the answer.. see if the 2 numbers add up to 22 and you are done!!!what i did: 13x + 6y= 167x= 5therefore, y= 175 adults + 17 kids = 22!!

Mitchell .
07-17-2007, 09:56 PM
This is a linear combination question.x = # of adultsy = # of kidsAdults pay \$13 and kids pay \$6 with \$167 total collected:13x + 6y =167The number of people (kids and adults) attending was 22:x+y=22Multiply the second equation by 6 (6x+6y=132) and then subtract from the first equation to eliminate y and solve for x. Then plug x into one of the original questions (I would go with the x+y=22) to solve for y: 13x + 6y =167- 6x +6y= 132----------------------7x = 35therefore x=5 and y =17Easy to check to since adults pay \$13 and kids pay \$6(13x5) + (6x17) = 16765 + 102 = 167167 = 167

Hari
07-17-2007, 10:35 PM
let the number of adults who attended the play be x.:. the no. of children=22-x( 13*x )+[(22-x)*6]=16713x+132-6x=1677x=35x=5:. 5 adults and 22-5=17 children attended the play.