Question

Two groups of people visited an amusement park. A group of

8 children and 4 adults paid $856 for their tickets. A different grou
of 2 children and 4 adults paid $508. What was the cost of a ticket
for an adult?

Answer 1

8.5 or 8.50

Explanation:

The cost of an adult ticket is $15.50 and the cost of a child ticket is $8.50

Proof:

Set up a system of equations calling Adults a and Children c

2a+3c= $56.50 (equation 1)

4c+a= $49.50 (equation 2)

a= -4c+49.50 (i subtracted 4c to both sides) (label equation 3)

sub equation 3 into equation 1

2(-4c+49.50)+3c= 56.50

-8c+99+3c=56.50

-5c+99=56.50

-99 -99

-5c = -42.50

c= -42.50/ -5

c= 8.50

sub c=8.50 into equation 3 to find adult price

a= -4(8.5)+49.50

a= 15.50

Therefore Child Cost = $8.50 and Adult Cost= $15.50

or

a=adult

c=child

Equation 1 (the first family)

2a+3c=56.5

Equation 2 (the second family)

a+4c=49.5 multiply by 2

2a+8c=99 multiply by -1

-2a-8c=-99

Systems of Equations

(2a+3c=56.5)

+ (-2a-8c=-99)

-------------

-5c=-42.5

c=$8.5

Substitute

2a+3*8.5=56.5

2a+25.5=56.5

2a=31

a=$15.5

Conclusion

Adult Ticket: $15.5

Child Ticket: $8.5