Question

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?

Answer 1

3 adult tickets and 4 kids tickets

Answer 2

Mr. Frankel bought 4 child tickets and 3 adult tickets

Data;

• 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

$x+y = 7...equation(i)\\4x+9y=43 ...equation(ii)$

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

$x+y=7\\x=7-y...equation(iii)$

Put equation(iii) into equation(ii)

$4x+9y=43\\x=7-y\\4(7-y)+9y=43\\28-4y+9y=43\\collect like terms\\5y=43-28\\5y=15\\y=3$

Put y = 3 into equation (i)

$x + y = 7\\y = 3\\x+3=7\\x = 4$

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

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