Office Max is offering a $40 rebate on all color printers. Sara is looking at a few different color printers that range in price from $165 to $295. How much can she to pay after the rebate?
Part A: Form a compound inequality to represent this problem and solve.
Part B: Can she stay with in her budget of $123 for the printer? Why or why not?
Part A: Forming a compound inequality to represent the problem:
Let's denote the original price of a color printer as \( P \). According to the problem, \( P \) can range from $165 to $295. With a $40 rebate, the price after the rebate would be \( P - 40 \). Therefore, our compound inequality with the rebate taken into account will be:
\( 165 - 40 \leq P - 40 \leq 295 - 40 \)
Simplifying the inequality:
\( 125 \leq P - 40 \leq 255 \)
Now let's solve for \( P \) to find the range of prices Sara will pay for a color printer after the rebate:
\( 125 + 40 \leq P \leq 255 + 40 \)
\( 165 \leq P \leq 295 \)
Therefore, after the $40 rebate, Sara can expect to pay between $165 and $295 for a color printer.
Part B: Based on Sara's budget of $123:
Looking at the solved inequality \( 165 \leq P \leq 295 \), we can see that the minimum amount she can expect to pay after the rebate is $165, which is already higher than her budget of $123. Therefore, Sara cannot stay within her budget of $123 for the color printer after applying the $40 rebate.