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?

8.5 or 8.50

Step-by-step 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

x = 12

y = 15

step-by-step explanation:

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.