Question

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?
|x - 645| = 20; maximum guess: 635 beans
|x - 645| = 20; maximum guess: 665 beans
|x - 20| = 645; maximum guess: 635 beans
|x - 20| = 645; maximum guess: 665 beans

Explanation:

Step1: Understand absolute - value equation concept

The distance between the guessed number $x$ and the actual number 645 should be within 20. The absolute - value equation for the distance between two numbers $a$ and $b$ is $|a - b|$. Here, $a=x$ and $b = 645$, so the equation is $|x - 645|=20$.

Step2: Solve the absolute - value equation

The absolute - value equation $|x - 645|=20$ can be written as two separate equations: $x-645 = 20$ or $x - 645=-20$.
For $x-645 = 20$, we solve for $x$ by adding 645 to both sides of the equation: $x=20 + 645=665$.
For $x - 645=-20$, we solve for $x$ by adding 645 to both sides of the equation: $x=-20 + 645 = 625$. The maximum value of $x$ is 665.

Answer:

B. $|x - 645| = 20$; maximum guess: 665 beans