[-/2 Points] DETAILS MY NOTES TGEIALG6 2.5.046. Show A and Show B are two television shows. The number of episodes of each show are consecutive integers whose sum is 225 . If there are more episodes of Show B, how many episodes of each were there? Show A episodes Show B SUBMIT ANSWER

Question

UpStudy AI · Accepted Answer

Let's denote the number of episodes of Show A as $$ a $$ and the number of episodes of Show B as $$ b $$. According to the problem, we have the following conditions:

1. The number of episodes of Show A and Show B are consecutive integers.
2. The sum of the episodes of both shows is 225.
3. Show B has more episodes than Show A.

From these conditions, we can express the relationships mathematically:

- Since $$ b $$ is greater than $$ a $$ and they are consecutive integers, we can write:
  $$
  b = a + 1
  $$

- The sum of the episodes is given by:
  $$
  a + b = 225
  $$

Now, we can substitute the expression for $$ b $$ into the sum equation:

$$
a + (a + 1) = 225
$$

This simplifies to:

$$
2a + 1 = 225
$$

Next, we will solve for $$ a $$:

1. Subtract 1 from both sides:
   $$
   2a = 224
   $$

2. Divide both sides by 2:
   $$
   a = 112
   $$

Now that we have $$ a $$, we can find $$ b $$:

$$
b = a + 1 = 112 + 1 = 113
$$

Thus, the number of episodes for each show is:

- Show A episodes: $$ 112 $$
- Show B episodes: $$ 113 $$

In conclusion, Show A has 112 episodes, and Show B has 113 episodes.
Show A has 112 episodes, and Show B has 113 episodes.

[-/2 Points] DETAILS MY NOTES TGEIALG6 2.5.046. Show A and Show B are two television shows. The number of episodes of each show are consecutive integers whose sum is 225 . If there are more episodes of Show B, how many episodes of each were there? Show A episodes Show B SUBMIT ANSWER

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Algebra Questions