Question

An Adult ticket at an amusement park costs $24.95 and a child's ticket costs $15.95. A group of 10 people paid $186.50 to enter the park. How many were adults

Answer 1

There were 3 adults

Explanation:

Step 1: Derive the first expression

a+c=10...equation 1

where;

a=number of adults

c=number of children

And total number of people=10

Step 2: Derive the second expression;

Total cost of tickets=(price per child ticket×number of children)+(price per adult ticket×number of adults)

where;

Total cost of tickets=$186.50

price per child ticket=$15.95

price per adult ticket=$24.95

number of children=c

number of adults=a

replacing;

(15.95×c)+(24.95×a)=186.5

24.95 a+15.95 c=186.5....equation 2

Step 3: Combine equation 1 and 2 and solve simultaneously

24.95 a+15.95 c=186.5

-

24.95(a+c=10)

(24.95 a-24.95 a)+(15.95 c-24.95 c)=186.5-(24.95×10)

-9 c=-63

c=-63/-9

c=7

replace the value for c in equation 1

a+c=10

a+7=10

a=10-7

a=3

There were 3 adults