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07172007  #1 
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Algebra problem anyone?
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.

07172007  #2 
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So let x be the number of adults. Then 22x is the number of children.The equation for the sales is:S = 13*x + 6*(22x) = 167 7x + 132 = 167 7x = 35 x = 5Therefore 5 adults and 17 children attended.

07172007  #3 
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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(22A) = 16713A + 132  6A = 1677A = 35A = 5C = 22  A = 22  5 = 17Check: 5 + 17 = 22 yep!13(5) + 6 (17) = 65 + 102 = 167 yep!

07172007  #4 
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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 22x, 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(22x) = $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 22x = 225 = 17

07172007  #5 
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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!!

07172007  #6 
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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= 1327x = 35therefore x=5 and y =17Easy to check to since adults pay $13 and kids pay $6(13x5) + (6x17) = 16765 + 102 = 167167 = 167

07172007  #7 
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let the number of adults who attended the play be x.:. the no. of children=22x( 13*x )+[(22x)*6]=16713x+1326x=1677x=35x=5:. 5 adults and 225=17 children attended the play.

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