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?
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.
To form a compound inequality, we can use the given information that Office Max is offering a $35 rebate on all color printers. Let's represent the range of prices for the printers as follows:
Let x represent the price of the color printer.
170 ≤ x ≤ 300
Now, we need to calculate how much Sara can plan to pay after the rebate.
To do this, subtract the $35 rebate from both sides of the inequality:
170 - 35 ≤ x - 35 ≤ 300 - 35
135 ≤ x - 35 ≤ 265
Next, we can simplify the compound inequality:
135 + 35 ≤ x ≤ 265 + 35
170 ≤ x ≤ 300
Therefore, Sara can plan to pay between $170 and $300 after the rebate.
Now, let's check if Sara can stay within her budget of $125 for the printer.
125 ≤ x
Comparing this inequality with the given range of prices, 170 ≤ x ≤ 300, we can see that $125 is less than the minimum price ($170) of the color printers Sara is looking at.
Therefore, she cannot stay within her budget of $125 for the printer.
To solve this problem, let's first set up a compound inequality to represent the situation.
Let x represent the price of the color printer Sara chooses.
Since she is eligible for a $35 rebate, she can plan to pay the price of the printer minus the rebate amount.
The compound inequality is:
170 ≤ x ≤ 300
Now, let's solve this compound inequality to find the acceptable range of x values.
For the lower bound, 170 ≤ x, Sara's printer choice must cost $170 or more.
For the upper bound, x ≤ 300, Sara's printer choice must cost $300 or less.
So, after the rebate, Sara can plan to pay any price between $170 and $300, inclusive.
Now let's check if Sara can stay within her budget of $125 for the printer.
Sara's budget is $125.
It is clear from the compound inequality that the lowest possible price for a printer is $170.
Therefore, Sara cannot stay within her budget of $125 because the lowest price printer exceeds her budget.
In conclusion, Sara can plan to pay anywhere from $170 to $300 after the rebate, but she cannot stay within her budget of $125.