Office Max is offering a $35 mail in rebate on all color printers. Sara is looking at a few different color printers that rang in price from $180 to $275. How much can she plan to pay after the rebate? Form a compoun inequality to represent this problem and solve. Can she stay with in her budget of $150 for the printer? Why or why not?
To form a compound inequality for this problem, let's denote the price of the color printer as x.
The rebate of $35 can be seen as a reduction of the price x, so we have x - 35 as the price after the rebate.
Given that the price of the color printer ranges from $180 to $275, we can write the inequalities:
$180 ≤ x ≤ $275
To find out if Sara can stay within her budget of $150, we need to check if the price after the rebate, x - 35, is less than or equal to $150:
x - 35 ≤ $150
Now we can solve the inequality:
Adding 35 to both sides of the inequality: x ≤ $150 + 35
x ≤ $185
From the given inequalities, we know that $180 ≤ x, so it is possible that x is less than or equal to $185. Therefore, it is possible for Sara to stay within her budget of $150 for the printer, but it depends on the specific prices of the color printers she is considering.
To form a compound inequality, we need to consider the range of printer prices. Let's assume the lowest price is represented by x and the highest price is represented by y.
The compound inequality can be expressed as follows: 180 ≤ x ≤ 275
Next, we need to consider the mail-in rebate. The mail-in rebate is $35, which means the final price after the rebate will be reduced by $35.
To find the price range after the rebate, we subtract $35 from both ends of the compound inequality:
145 ≤ x - 35 ≤ 240
Now, let's check if Sara can stay within her budget of $150 for the printer.
To determine if a printer price is within her budget, we need to check if the price range after the rebate is also within her budget. Since 145 ≤ x - 35 ≤ 240, we need to determine if x - 35 ≤ 150.
If we add 35 to both sides, we have:
x - 35 + 35 ≤ 150 + 35
Simplifying:
x ≤ 185
Based on this information, if the lowest price (x) is equal to or less than $185, Sara can stay within her budget of $150 for the printer. If x is greater than $185, she will exceed her budget.
To form a compound inequality to represent Sara's situation, we can use the following information:
Let's assume the price of the color printer Sara chooses is represented by "x."
First, we need to consider the price range of the printers Sara is looking at: $180 to $275. This can be expressed as the inequality:
180 ≤ x ≤ 275
Next, we need to account for the $35 mail-in rebate offered by Office Max. To calculate the final price, we need to subtract the rebate from the original price of the printer. So, the final price, after the rebate, can be expressed as:
x - 35
To determine if Sara can stay within her budget of $150, we need to check if the final price (x - 35) is less than or equal to $150. This can be expressed as an inequality:
x - 35 ≤ 150
Now, we have formed a compound inequality to represent Sara's situation:
180 ≤ x ≤ 275 and x - 35 ≤ 150
To solve this compound inequality, we need to find the overlapping range of values that satisfy both conditions.
First, let's solve the second inequality:
x - 35 ≤ 150
x ≤ 185
Now, we need to find the overlapping range between 180 ≤ x ≤ 275 and x ≤ 185.
The highest value that satisfies both conditions is x = 185.
Therefore, Sara can stay within her budget of $150 if the price of the printer she chooses is $185 or less. If the price of the color printer exceeds $185, it will be out of her budget.