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?
To represent the problem, we can set up a compound inequality with the cost of the color printer after the rebate.
Let x be the cost of the color printer.
The rebate offered by Office Max is $35.
After the rebate, the cost of the printer will be x - $35.
The compound inequality can be written as:
$170 ≤ x ≤ $300 (range of prices for the color printers)
To find out how much Sara can plan to pay after the rebate, we subtract $35 from the range of prices:
$170 - $35 ≤ x - $35 ≤ $300 - $35
$135 ≤ x - $35 ≤ $265
Hence, after the rebate, Sara can plan to pay a price between $135 and $265 for the color printer.
To check if she can stay within a budget of $125, we compare the lowest price after the rebate ($135) to her budget:
$125 ≤ $135
Since $125 is less than $135, Sara can stay within her budget of $125 even after the rebate.
To form a compound inequality for this problem, let's assume the price of the color printer that Sara chooses is represented by x. The inequality can be formed as follows:
$170 ≤ x ≤ $300
To find out how much Sara can plan to pay after the rebate, we subtract the rebate amount of $35 from the lower and upper bounds of the inequality:
$170 - $35 ≤ x - $35 ≤ $300 - $35
Simplifying:
$135 ≤ x ≤ $265
Therefore, Sara can plan to pay between $135 and $265 after the rebate.
As for whether she can stay within a budget of $125 for the printer, we compare the budget amount to the range of prices after the rebate:
$135 ≤ $125 ≤ $265
Since $125 is not within the range of prices after the rebate, Sara cannot stay within a budget of $125 for the printer.
To calculate how much Sara can expect to pay after the rebate, we can subtract the rebate amount from the original price of each printer.
Let's assume the original prices of the printers are represented by the variable 'x.' The rebate amount is $35. Therefore, the amount Sara can expect to pay after the rebate, 'y,' can be calculated using the formula y = x - 35.
Now, we need to form a compound inequality to represent the range of original prices of the printers and solve it to find the possible values of 'x' (original prices).
Considering the range of prices from $170 to $300, we can write the compound inequality as follows:
170 ≤ x ≤ 300
To solve this compound inequality, we need to apply the same operations to both sides of the inequality.
Subtracting 35 from all parts of the compound inequality, we have:
170 - 35 ≤ x - 35 ≤ 300 - 35
135 ≤ x - 35 ≤ 265
To isolate 'x,' we add 35 to all parts of the compound inequality:
135 + 35 ≤ x - 35 + 35 ≤ 265 + 35
170 ≤ x ≤ 300
Hence, the range of possible values for 'x' (original prices) falls between $170 and $300.
However, Sara wants to stay within a budget of $125 for the printer. We need to determine whether any price within the range of $170 to $300 is below $125.
Checking the range, we find that none of the possible values for 'x' satisfy the condition of being below $125. Therefore, Sara cannot stay within her budget of $125 for the printer.
In summary, Sara can expect to pay a price between $170 and $300 after the rebate, but none of these options fit within her budget of $125.