Given (a+2,a-2)= a for all integers a, (6,2)=

a) 3
b) 4
c) 5
d) 6
e) 8

The cost of a drive-in movie is $y per vehicle. A group of friends in a van shared the admission cost by paying $0.40 each.If 6 more friends had gone along,everyone would have paid only $0.25 each. What is the value of $y?

a) 4
b) 6
c) 8
d) 10
e) 12

1.

Solve for a
a+2=6
a-2=2

2.
Let x=initial number of friends.
0.4x = 0.25(x+6)
Solve for x.

To find the value of (6,2), we need to substitute the values of a and simplify the expression (a+2, a-2).

Given that (a+2, a-2) = a for all integers a, we can substitute a=6 into the expression.

(6+2, 6-2) = 6

Simplifying, we get (8, 4) = 6

Therefore, the value of (6,2) is 6.

The answer to the first question is:
b) 4

For the second question, let's assume the total cost of the drive-in movie is C.

According to the given information, a group of friends in a van shared the admission cost by paying $0.40 each. This means the total cost is equal to the number of friends (let's say n) multiplied by $0.40:
C = n * $0.40

If 6 more friends had gone along, everyone would have paid $0.25 each. This means the total cost is equal to the new number of friends (n+6) multiplied by $0.25:
C = (n + 6) * $0.25

We can set up a system of equations to solve for n and C.

Equation 1: C = n * $0.40
Equation 2: C = (n + 6) * $0.25

We can substitute Equation 1 into Equation 2:
n * $0.40 = (n + 6) * $0.25

Simplifying, we get:
0.40n = 0.25n + 1.50

Subtracting 0.25n from both sides:
0.15n = 1.50

Dividing both sides by 0.15:
n = 10

Now that we have found the value of n (the number of friends), we can substitute it back into one of the equations to find the value of C (the total cost).

Using Equation 1:
C = 10 * $0.40
C = $4

Therefore, the value of $y is:
a) 4