Mr. Frankel bought 7 tickets to a puppet show and spent $43. He bought a combination of child tickets for $4 each and adult tickets for $9 each. Which system of equations below will determine the number of adult tickets, a, and the number of child tickets, c, he bought?

2 Answer

  • 3 adult tickets and 4 kids tickets

  • Mr. Frankel bought 4 child tickets and 3 adult tickets


    • Total number of ticket = 7
    • Total amount spent =$43
    • cost of child ticket = $4
    • cost of adult ticket = $9

    To solve this problem, we would write a system of equation representing the word problem.

    System of Equation

    These are two or more mathematical statements, written to explain a word problem better.

    Let x represent the number of child ticket

    let y represent the number of adult ticket

    [tex]x+y = 7...equation(i)\\4x+9y=43 ...equation(ii)[/tex]

    From equation(i), let's make x the subject of formula


    Put equation(iii) into equation(ii)

    [tex]4x+9y=43\\x=7-y\\4(7-y)+9y=43\\28-4y+9y=43\\collect like terms\\5y=43-28\\5y=15\\y=3[/tex]

    Put y = 3 into equation (i)

    [tex]x + y = 7\\y = 3\\x+3=7\\x = 4[/tex]

    From the calculations above, Mr. Frankel bought 4 child tickets and 3 adult tickets.

    Learn more on system of equations here;