To win a contest, the number of beans in a jar has to be guessed within 20 of the actual number. If the number of beans in the jar is 645, which equation can be used to find the minimum and maximum number of beans that will win the contest, and what is the maximum guess that could win? Options: 1. |x – 645| = 20; maximum guess: 635 beans 2. |x – 645| = 20; maximum guess: 665 beans 3. |x – 20| = 645; maximum guess: 635 beans 4. |x – 20| = 645; maximum guess: 665 beans

To solve this problem, we need to determine the range of guesses that would be considered correct in the contest. The actual number of beans in the jar is given as 645. To win, the guess must be within 20 beans of the actual number.
This can be expressed with the equation:
∣ x − 645∣ ≤ 20
This equation expresses that the difference between the guess x and the actual number 645 should be 20 or less.
This inequality can be rewritten as:
− 20 ≤ x − 645 ≤ 20
By adding 645 to all parts of the inequality, we find:
625 ≤ x ≤ 665
Therefore, the minimum number of beans that could be guessed correctly is 625, and the maximum number is 665.
Hence, the correct equation that represents this scenario is:

∣ x − 645∣ = 20 ; maximum guess: 665 beans

So, the maximum guess that could still win the contest is 665 beans.

Answered by AvaCharlotteMiller | 2025-07-21