Question

Write a system of equations to solve the problem. A local theatre sells out for their show. They sell all 500 tickets for a total purse of $8,070.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults. If the band sold three times as many adult tickets as children's tickets, how many of each type were sold? student children adult tickets tickets tickets

Answer 1

Let,

x= Numbers of student tickets sold at $15

y= Number of children tickets sold at $12

z= Number of adult tickets sold at $18

Total Number of tickets=x+y+z But, total number of tickets sold=500 [Given] => x+y+z=500....................................(i)

Total amount of tickets sold= $(15x+12y+18z) But, total number of tickets sold=$8070 [Given] => (15x+12y+18z)=8070......................(ii)

Number of adult tickets sold is 3 times that of the children tickets => 3y=z.................................................(iii)

From (i) & (iii), x+y+3y=500 => x+4y=500..............................................(iv)

From (ii) & (iii), 15x+12y+18(3y)=8070 => 15x+12y+54y=8070 => 15x+66y=8070........................................(v)

(iv)*15-(v), 60y-66y=7500-8070 => -6y=-570 => y=95

Put y=95 in (iv), => x+4(95)=500 => x+380=500 => x=120

Put x=120 & y=95 in (i), 120+95+z=500 => z=285

x= Numbers of student tickets sold at $15=120 y= Number of children tickets sold at $12=95 z= Number of adult tickets sold at $18=285

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