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 can she plan to pay after the rebate?
Part A: Form a compound inequality to represent this problem and solve.
Part B: Can she stay within her budget of $125 for the printer? Why or Why not?
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Part A:
Let's assume the price of the color printer is represented by the variable x.
The given information states that Office Max is offering a $35 rebate on all color printers. This means, after the rebate, Sara will have to pay the remaining cost of the printer.
To calculate the remaining cost, we subtract the rebate from the price of the printer:
Remaining cost = Price of the printer - Rebate = x - $35
The problem states that the price of the color printers range from $170 to $300. So we can write the following inequality:
$170 ≤ x ≤ $300
Now we can substitute the value of x in the inequality above with the remaining cost:
$170 ≤ x ≤ $300
$170 ≤ (x - $35) ≤ $300
Simplifying the inequality:
$170 + $35 ≤ x ≤ $300 + $35
$205 ≤ x ≤ $335
Therefore, the compound inequality to represent the problem is:
$205 ≤ x ≤ $335
Part B:
Sara's budget for the printer is $125. We need to determine if any of the prices within the range $205 to $335 fall within her budget.
If x represents the price of the printer, and the remaining cost after the rebate is x - $35, then we can set up the inequality:
x - $35 ≤ $125
Simplifying the inequality:
x ≤ $125 + $35
x ≤ $160
Therefore, all color printers within the price range of $205 to $335 are more expensive than Sara's budget of $125. Therefore, she cannot stay within her budget.
Part A: To calculate the price after the rebate, we will subtract the rebate amount of $35 from the original price of the color printer.
Let's assume the original price of the printer is x dollars.
After deducting the $35 rebate, the price becomes (x - 35) dollars.
To form a compound inequality for the range of color printers that Sara is considering, we'll use the given price range of $170 to $300.
Therefore, the compound inequality representing the price range after the rebate would be:
170 ≤ x - 35 ≤ 300
Now, we solve for x:
First, we add 35 to all parts of the inequality:
170 + 35 ≤ x - 35 + 35 ≤ 300 + 35
205 ≤ x ≤ 335
Therefore, the value of x (the original price of the printer) needs to fall between $205 and $335 to satisfy the given conditions.
Part B: Sara's budget for the printer is $125. We need to determine if any of the color printers fall within this budget after the rebate.
To find out, we substitute x = 125 into the compound inequality we formed in Part A:
205 ≤ 125 ≤ 335
This inequality is not true because 125 is not between 205 and 335. So, Sara cannot stay within her budget of $125 for any of the color printers, even after the rebate.
Hence, she needs to consider other options or increase her budget in order to purchase a color printer.
Part A:
Let's assume the price of the color printer as "x." After the $35 rebate, Sara will have to pay (x - $35).
The price range of the color printers is from $170 to $300 inclusive. Hence, the compound inequality representing this problem is:
170 ≤ (x - $35) ≤ 300
To solve this compound inequality, we will first add $35 to all parts of the inequality:
170 + $35 ≤ (x - $35) + $35 ≤ 300 + $35
205 ≤ x ≤ 335
Therefore, the price of the printer (x) must be between $205 and $335 after the rebate.
Part B:
Sara's budget for the printer is $125. We need to check whether a price within this range is possible after the rebate.
Since the price must be between $205 and $335 after the rebate, it means the printer must cost less than $205 before the rebate. But Sara's budget is only $125.
Hence, she cannot stay within her budget of $125 for the printer, as the cost of the printer after the rebate will exceed her budget.