Question

A student needs to buy notebooks (\(n\)) for a semester. Double the number of notebooks plus \(5\) must strictly exceed \(15\), but the number of notebooks plus \(10\) must be no more than \(22\). What is the range of notebooks they can buy?

• A. \(\{5,6,7,8,9,10,11,12\}\)
• B. \(\{6,7,8,9,10,11\}\)
• C. \(\{6,7,8,9,10,11,12\}\)
• D. \(\{5,6,7,8,9,10,11,12,13,14,15\}\)

Hint:

For simultaneous inequalities, solve each inequality separately and then find the common interval satisfying both conditions.

Answer 1

The Correct Option is C

Concept: This problem involves solving simultaneous inequalities. We solve each inequality separately and then combine the obtained ranges.

Step 1: Form the first inequality. Given: \[ 2n+5>15 \] Subtract \(5\): \[ 2n>10 \] Divide by \(2\): \[ n>5 \]

Step 2: Form the second inequality. Given: \[ n+10\le22 \] Subtract \(10\): \[ n\le12 \]

Step 3: Combine the inequalities. We have: \[ 5<n\le12 \] Since the number of notebooks must be a whole number, \[ n=\{6,7,8,9,10,11,12\} \] Thus, \[ \boxed{\{6,7,8,9,10,11,12\}} \]