Question

Sally bought a few boxes of chocolates. She gave 2 to her younger sister. She had at most 5 boxes left. Write an inequality to find how many chocolate boxes did she buy? Define your variable. Explain why you chose the inequality sign that you did.

Answer 1

Let \( x \) represent the number of chocolate boxes Sally bought. The inequality representing the scenario is
`\( x - 2 \leq 5 \)` , where \( x \) represents the total number of boxes she bought, subtracting the 2 she gave away and ensuring the remaining boxes are at most 5.

Explanation:

To solve this problem, we use the variable \( x \) to represent the number of chocolate boxes Sally bought initially. She gave 2 boxes to her sister, so the number of boxes remaining should be at most 5. Mathematically, this can be represented as \
`( x - 2 \leq 5 \)` , where \( x - 2 \) accounts for the boxes she had after giving away 2, and the inequality states that this quantity should be less than or equal to 5.

Choosing the "less than or equal to"
`(\(\leq\))` sign is appropriate because Sally can have at most 5 boxes left after giving away 2. The inclusion of the "equal to" part allows for the scenario where Sally has exactly 5 boxes left after giving away 2, satisfying the condition of having at most 5 boxes remaining. Thus, the inequality
`\( x - 2 \leq 5 \)` effectively represents the situation where Sally bought a certain number of boxes, gave away 2, and had at most 5 boxes left.

Answer 2

Let x represent the original number of chocolate boxes Sally bought. The inequality to find the possible values of x is x - 2
`\leq` 5 , where x is the number of chocolate boxes Sally initially bought.

Step-by-step explanation:

To solve this problem, let's define a variable to represent the number of chocolate boxes Sally bought. Let x be the original number of boxes. After giving 2 boxes to her younger sister, she had at most 5 boxes left. This can be expressed as x - 2
`\leq` 5 .

The inequality x - 2
`\leq` 5 is chosen to ensure that Sally has at most 5 boxes left. If we add 2 to both sides of the inequality x - 2 + 2
`\leq` 5 + 2 , we get x
`\leq` 7 . This means Sally initially bought at most 7 boxes of chocolates.

Now, let's check the validity of the inequality. If Sally bought 7 boxes x = 7 , after giving 2 to her sister, she would have 7 - 2 = 5 boxes left, satisfying the condition. If Sally bought fewer boxes, the condition still holds. However, if she bought more than 7 boxes, the inequality would not be true, violating the given scenario.

In conclusion, the inequality x - 2
`\leq` 5 with x
`\leq` 7 accurately represents the possible values for the number of chocolate boxes Sally bought, ensuring she had at most 5 boxes left after giving 2 to her younger sister.