Show A and Show B are two of the most popular television shows of all time. The number of episodes of each show are consecutive even integers whose sum is 570. If there are more episodes of Show A, how many episodes of each were there?

A = 286 episodes

B = 284 episodes

Step-by-step explanation:

Let n = the of show B

    n + 2 = the of show A

Therefore, according to the question,

The sum of the number of the episodes of each show are consecutive even integers  = 570

Therefore,

n + n + 2 = 570

2n + 2 = 570

2n = 568

n = 284

Therefore, the number of episodes for B = 284

The number of episodes for A = n + 2 = 284 + 2

                                                              = 286

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions