document.write( "Question 78321: Tickets for a play at the community theater cost $16 for an adult and $2 for a child. If 210 tickets were sold and the receipts were $2380, how many of each type of ticket were sold? \n" ); document.write( "

Algebra.Com's Answer #56152 by rmromero(383) $\"\"$ $\"About$

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document.write( "Tickets for a play at the community theater cost $16 for an adult and $2 for a child. If 210 tickets were sold and the receipts were $2380, how many of each type of ticket were sold?\r
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document.write( "What is asked in the problem?
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document.write( "    How many of each type of tickets were sold?\r
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document.write( "Given:
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document.write( "Tickets for a play at the community theater cost $16 for an adult 
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document.write( "and $2 for a child. 
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document.write( "If 210 tickets were sold and the receipts were $2380.\r
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document.write( "Representation:
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document.write( "Let x be the number of tickets sold for adults
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document.write( "    y be the number of tickets sold for kids\r
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document.write( "Equations:
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document.write( "The tickets sold were 210. adult's tickets plus children's ticket
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document.write( "   x + y = 210\r
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document.write( "The receipt cost 2380. Adults' ticket cost $16 and children's $2.
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document.write( "  16x + 2y = 2380\r
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document.write( "Solve the system of equations\r
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document.write( "    x +  y = 210        
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document.write( "  16x + 2y = 2380
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document.write( "Multiply -2 to x + y = 210 to eliminate y then add the 2 equations\r
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document.write( "  -2x - 2y = -420        
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document.write( "  16x + 2y = 2380
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document.write( "   14x     = 1960     Divide both sides by 14
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document.write( "         x = 140      there are 140 adult tickets sold\r
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document.write( "Choose either of the 2 equation. Substitute the value of x to find y.\r
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document.write( "   x + y = 210
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document.write( " 140 + y = 210
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document.write( "       y = 210 - 140
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document.write( "       y = 70            There are 70 children tickets sold.\r
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document.write( "Checking\r
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document.write( "    x + y = 210 ; x = 140 & y = 70
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document.write( " 140 + 70 = 210 
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document.write( "      210 = 210    True\r
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document.write( "         16x + 2y = 2380
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document.write( "16 (140) + 2 (70) = 2380
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document.write( "       2240 + 140 = 2380
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document.write( "             2380 = 2380    True\r
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document.write( "Therefore the solution we have is correct x = 140 and y = 70. There are 140 adult tickets sold and 70 children tickets sold.\r
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document.write( "Rmromero
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