office max is offering a $35 rebate on all color printers. Sara is looking at a few different color printers that range in price from $170 to $300. How much can she plan to pay after the rebate?

form a compound inequality to represent this problem and solve.

can she stay with in budget of $125 for the printer why or why not?

1 answer

Let's assume that the price of the color printer Sara chooses is represented by the variable p.

According to the problem, Sara is looking at printers that range in price from $170 to $300. To represent this range of prices, we can write the compound inequality:

$170 ≤ p ≤ $300

To find out how much Sara can plan to pay after the rebate, we need to subtract the $35 rebate from the price of the printer. This can be represented as:

p - $35

Now, let's solve for the range of prices Sara can plan to pay after the rebate.

For the minimum price ($170), we have:

p - $35 ≥ $170

Adding $35 to both sides of the inequality:

p ≥ $170 + $35

p ≥ $205

For the maximum price ($300), we have:

p - $35 ≤ $300

Adding $35 to both sides of the inequality:

p ≤ $300 + $35

p ≤ $335

So, after the rebate, Sara can plan to pay between $205 and $335 for the color printer.

Now, let's consider if she can stay within a budget of $125 for the printer.
If Sara's budget is $125, we need to determine if there is a value of p that satisfies the compound inequality:

$205 ≤ p ≤ $335

Let's try the lowest value in the range ($205):

$205 ≤ $125

This inequality is NOT true, meaning she cannot stay within her budget of $125.

Therefore, Sara cannot stay within a budget of $125 for the printer.