Question

HOTELS The Lincoln's hotel room costs $90 a night. An additional 10% tax is added.

Hotel parking is $12 per day. The Lincoln's expect to spend $30 in tips during their stay.
Solve the inequality 90x + 90(0.1)× + 12x + 30 ≤ 600 to find how many nights the Lincoln's can stay at the hotel without exceeding total hotel costs of $600.

Answer 1

Inequality answer: x ≤ 5.5

Answer in context:

You can't stay a part of a night, meaning we must round 5.5 down to 5. Therefore, the Lincolns can only stay 5 nights in order to not exceed a total hotel cost of $600.

Explanation:

Step 1: Distribute the 90 and combine like terms on the left-hand side:

90x + 12x + (90 * 0.1) + 30 ≤ 600

102x + 9 + 30 ≤ 400

102x + 39 ≤ 600

Step 2: Subtract 39 from both sides:

(102x + 39 ≤ 600) - 39

102x ≤ 561

Step 3: Divide both sides by 102 to solve for x:

(102x ≤ 561) / 102

x ≤ 5.5

Since the Lincons can't stay a fraction of the night, we must round down to 5.

Therefore, they can stay no more than 5 nights in order to not exceed a total hotel cost of $600.

Answer 2

Answer: They can stay five days.

Step-by-step explanation: Pic (I just worked out the problem on paper.)