Question

John told his sister Olivia that "Mike would give her at least $\$3$ but not more than $\$6$. What is/are the possible value(s) that Mike gives?

• A. 3
• B. 4
• C. 6
• D. 7

Answer 1

Answer: (A), (B), (C)

6

Let $x$ represent the amount of money given by Mike to Olivia.
Given, $x$ is at least $\$3$ and not more than $\$6$.

Step 1: $x$ is at least $\$3$.
Hence, $x$ can have any value which is greater than or equal to $3$.

The above statement is mathemtical representated as: $x\ge 3$ which can also be written as $3\le x$

It can be represented in the number line as:
A closed circle at $3$ and the red line goes to the right, indicating that $x$ is greater than $3.$

Step 2: $x$ is not more than 6.
Hence, $x$ can have any value which is less than or equal to $6$.

The above statement is mathemtical representated as: $x\le 6$

It can be represented in the number line as:
A closed circle at $6$ and the red line goes to the left, indicating that $x$ is less than $6.$

Combinig both the inequality:
$3\le x\le 6$
It can be represented in the number line as:

Value of $x$ which varies from 3 to 6 can be accepted.
Option (a): $x=3$
3 lies between the possible values of $x$.
Accepted

Option (b): $x=4$
4 lies betweem the possible values of $x$.
Accepted

Option (c): $x=6$
6 lies between the possible values of $x$.
Accepted

Option (d): $x=7$
7 do not lie between the possible values of $x$.
Rejected