Office Max is offering $40 mail in rebate on all Office chairs. George is looking at a few different office chairs that range in price from $195 to $300. How much can he plan to pay after the rebate? Form a compound inequality to represent this problem and solve. Can he stay within his $150 budget for the office chair? Why or why not?
Let x be the price of the office chair.
The compound inequality is: 195 ≤ x ≤ 300.
George can plan to pay after the rebate: x - $40.
If the price of the office chair is $195, George can plan to pay $195 - $40 = $<<195-40=155>>155 after the rebate.
If the price of the office chair is $300, George can plan to pay $300 - $40 = $<<300-40=260>>260 after the rebate.
Since both $155 and $260 are within his $150 budget, he can stay within his budget for the office chair. Answer: \boxed{\text{Yes}}.
explain
I apologize for the incorrect answer. Let me correct myself.
Let x be the price of the office chair.
According to the problem, the mail-in rebate is $40. Therefore, the amount George can plan to pay after the rebate is (x - $40).
George has a budget of $150 for the office chair. In order to stay within this budget, we can write the inequality:
(x - $40) ≤ $150
Now, we need to solve this inequality to determine the possible range of prices for the office chair.
Adding $40 to both sides of the inequality, we get:
x ≤ $190
So, the price of the office chair has to be less than or equal to $190 in order for George to stay within his budget.
Now let's consider the range of prices for the office chair that George is looking at, which is $195 to $300.
If the price of the office chair is $195, then (x - $40) = ($195 - $40) = $155, which is within his budget.
If the price of the office chair is $300, then (x - $40) = ($300 - $40) = $260, which is within his budget as well.
Therefore, George can stay within his $150 budget for the office chair, since the price range he is considering ($195 to $300) guarantees that he will be able to pay less than or equal to $190 after the rebate.
To determine how much George can expect to pay after the mail-in rebate and whether he can stay within his $150 budget, we can form a compound inequality and solve it.
Let's assume "x" represents the price of the office chair, then the compound inequality is:
$195 ≤ x ≤ $300
To find out how much George can expect to pay after the rebate, we subtract the $40 rebate amount from the price of the office chair.
So the adjusted compound inequality is:
$195 - $40 ≤ x - $40 ≤ $300 - $40
Simplifying further:
$155 ≤ x - $40 ≤ $260
Next, we add $40 to each side of the inequality:
$155 + $40 ≤ x - $40 + $40 ≤ $260 + $40
Simplifying:
$195 ≤ x ≤ $300
Now that we have the simplified inequality, we can conclude that George can expect to pay between $195 and $300.
To determine if he can stay within his $150 budget, we check if $150 falls within this range:
$195 ≤ $150 ≤ $300
Since $150 is not between $195 and $300, George cannot stay within his $150 budget to purchase any of the office chairs available.