Question

write and solve a system of equations. show work on your recording sheet. enter answer here. bob bought 24 hockey tickets for $83. adult tickets cost $5.50 and child tickets cost $2.00. how many of each did he buy? bob bought 95 adult tickets and 12 child tickets.

Explanation:

Step1: Define variables

Let $a$ = number of adult tickets, $c$ = number of child tickets.

Step2: Set up total tickets equation

$a + c = 24$

Step3: Set up total cost equation

$5.50a + 2.00c = 83$

Step4: Isolate $a$ from Step2

$a = 24 - c$

Step5: Substitute into cost equation

$5.50(24 - c) + 2c = 83$

Step6: Expand and simplify

$132 - 5.5c + 2c = 83$
$132 - 3.5c = 83$

Step7: Solve for $c$

$-3.5c = 83 - 132$
$-3.5c = -49$
$c = \frac{-49}{-3.5} = 14$

Step8: Solve for $a$

$a = 24 - 14 = 10$

Answer:

Bob bought $\boldsymbol{10}$ adult tickets and $\boldsymbol{14}$ child tickets.