Question

The number of home team fans was seven more than four times the number of visiting team fans at a softball game. If there were 142 more home team fans than visiting team fans, how many total fans were at the game?

Please include work!

Answer 1

The number of home team fans was 187 and the number of visiting team fans was 45, making a total of 232 fans at the game.

Step-by-step explanation:

Let's assume the number of visiting team fans as x.

According to the given information, the number of home team fans is seven more than four times the number of visiting team fans. So, we can write the equation as:

Home team fans = 4x + 7

Also, it is mentioned that there were 142 more home team fans than visiting team fans. So, we can write another equation as:

Home team fans - Visiting team fans = 142

Substituting the value of home team fans from the first equation into the second equation:

(4x + 7) - x = 142

Simplifying the equation:

4x - x + 7 = 142

3x + 7 = 142

3x = 135

x = 45

Now, we can find the number of home team fans by substituting the value of x back into the first equation:

Home team fans = 4(45) + 7 = 187

So, the total number of fans at the game is the sum of home team fans and visiting team fans:

Total fans = Home team fans + Visiting team fans = 187 + 45 = 232.

Answer 2

Let's start by using variables to represent the number of home team fans (H) and the number of visiting team fans (V).

From the problem, we know that:

H = 4V + 7 (the number of home team fans was seven more than four times the number of visiting team fans)

H = V + 142 (there were 142 more home team fans than visiting team fans)

We can use substitution to solve for one of the variables. Substituting the first equation into the second equation, we get:

4V + 7 = V + 142

Simplifying this equation, we get:

3V = 135

V = 45

Now that we know the number of visiting team fans, we can use the first equation to solve for the number of home team fans:

H = 4V + 7 = 4(45) + 7 = 187

Therefore, there were a total of:

H + V = 187 + 45 = 232

fans at the game.