Question

b-116. write a system of two equations to solve this problem. then solve the system. an adult ticket to the amusement park cost $24.95 and a child’s ticket cost $15.95. a group of 10 people paid $186.50 to enter the park. how many were adults?

Explanation:

Step1: Define variables

Let $a$ = number of adults, $c$ = number of children.

Step2: Total people equation

Total group size is 10:
$a + c = 10$

Step3: Total cost equation

Total cost is sum of ticket costs:
$24.95a + 15.95c = 186.50$

Step4: Isolate $c$ from Step2

$c = 10 - a$

Step5: Substitute $c$ into cost equation

$24.95a + 15.95(10 - a) = 186.50$

Step6: Expand and simplify

$24.95a + 159.5 - 15.95a = 186.50$
$9a + 159.5 = 186.50$

Step7: Solve for $a$

$9a = 186.50 - 159.5$
$9a = 27$
$a = \frac{27}{9} = 3$

Answer:

3