If in a football match, $\frac{1}{6}$ part of the spectators of a football match, sit under the shade while 4000 in open. Then how many spectators were in all?

Question

Accepted Answer

To determine the total number of spectators at the football match, we need to consider the information given: $\frac{1}{6}$ of the spectators are sitting under the shade, while 4000 spectators are sitting in the open.

Let's denote the total number of spectators as $ x $.

According to the problem, $\frac{1}{6}$ of the spectators are under the shade, which means the remaining $\frac{5}{6}$ of the spectators are sitting in the open. We know that the number of spectators sitting in the open is 4000. Therefore, we can set up the equation:

$$
\frac{5}{6}x = 4000
$$

To find $ x $, we solve the equation:

$$
x = \frac{4000 \times 6}{5}
$$

$$
x = \frac{24000}{5}
$$

$$
x = 4800
$$

Thus, the total number of spectators is 4800, which corresponds to Option 3.

Now, let's explain why the other options are incorrect:

1. **Option 1 (4500):** If the total number of spectators were 4500, then $\frac{5}{6}$ of 4500 would be 3750, not 4000. Therefore, this option does not satisfy the condition that 4000 spectators are sitting in the open.

2. **Option 2 (4400):** If the total number of spectators were 4400, then $\frac{5}{6}$ of 4400 would be approximately 3667, not 4000. This option also fails to meet the condition of 4000 spectators in the open.

3. **Option 4 (4200):** If the total number of spectators were 4200, then $\frac{5}{6}$ of 4200 would be 3500, not 4000. This option does not satisfy the given condition either.

Therefore, the only option that correctly satisfies the condition of 4000 spectators sitting in the open is Option 3, which is 4800 total spectators.