Question

EMERGENCY!!! OK SO I need help on 4 questions! Lots of points for this :) Also please make sure it's correct cause this is for a grade! Please and thank you so much! :D
1. Erika estimates that she is 200 to 300 miles away from her destination. If her car travels 25 miles per gallon of gas and each gallon costs $4.00, what is the best estimate for the amount of money, x, that Erika has to pay to get to her destination? A. 24≤x≤38
B. 64≤x≤82
C. 12≤x≤18
D. 32≤x≤48


2. Consultant A chargers $160 for the first hour and $75 per hour after the first. Consultant B charger a flat rate of $90 per hour. Consultant C charges $140 for the first hour and $80 per hour after the first. For a five hour session, which consultant offers the cheapest price? A. Consultant A
B. Consultant B
C. Consultant C
D. All three offer the same price.

3. A hotel chargers $225 per night to rent a suite. The hotel also charges $75 per day for full room service. If Jessica and Ashely purchased full room service for every night they stayed at the hotel and spent a total of $1,200, how many nights did they stay at the hotel? A. 3
B. 4
C. 5
D. 6

4. A certain ride at an amusement park requires that children be at least 50 inches tall but no more that 65 inches tall. Which of the following absolute values best represents this restriction, where ( h ) represents height?
A. |h−57.5|≤7.5
B. |h+7.5|≤65
C. |h+50|≤65
D. |h+65|≤50

Answer 1

                               Question # 1 Solution

Answer:

32≤x≤48 is the best estimate for the amount of money, x, that Erika has to pay to get to her destination. Hence, option D is correct.

Step-by-step Explanation:

Information Fetching and Solution Steps

• Erika estimates that she is 200 to 300 miles away from her destination
• Car travels 25 miles per gallon of gas
• Cost of each gallon being $4.00

As Erika estimates that she is 200 to 300 miles away from her destination, and car travels 25 miles per gallon of gas. So,

• First dividing 200 by 25 to get the number of gallons a car needed to make 200 miles

        i.e 200/25 = 8 gallons.

        As cost of each gallon being $4.00.

        So, 8 × 4 = 32$ is the amount she needed to make 200 miles.

• Then dividing 300 by 25 to get the number of gallons a car needed to make 300 miles

        i.e 300/25 = 12 gallons.

        As cost of each gallon being $4.00.

        So, 12 × 4 = 48$ is the amount she needed to make 300 miles.

From the above calculation, we observe that 32$ and 48$ is the best estimate between 200 miles and 300 miles.

Therefore, 32≤x≤48 is the best estimate for the amount of money, x, that Erika has to pay to get to her destination. Hence, option D is correct.

                                   Question # 2 Solution

Answer:

Consultant B offers the cheapest price for a five hour session.

Hence, B. Consultant B is the correct option.

Step-by-step Explanation:

Analyzing the offer price of Consultant A, B and C for a Five hour session:

• Consultant A chargers $160 for the first hour

• $75 per hour after the first.

So, for five hour session, Consultant A is offering the price:

$160 + $75 + $75 + $75 + $75 = $460

• Consultant B chargers a flat rate of $90 per hour

So, for five hour session, Consultant B is offering the price:

$90 + $90 + $90 + $90 + $90 = 450 US$

• Consultant C chargers $140 for the first hour

• $80 per hour after the first.

So, for five hour session, Consultant C is offering the price:

$140 + $80 + $80 + $80 + $80 = $460

Comparing the price offers of Consultant A, B and C

So, by comparing the price offers of Consultant A, B and C, we determine that:

• Consultant A is offering the price $460 for five hour session.
• Consultant B is offering the price $450 for five hour session.
• Consultant C is offering the price $460 for five hour session.

So, from this comparison, we conclude that Consultant B offers the cheapest price for a five hour session.

Hence, B. Consultant B is the correct option.

                             

                             Question # 3 Solution

Answer:

They spent 4 nights at the hotel. Hence, option B is correct.

Step-by-step Explanation:

To determine:

how many nights did they stay at the hotel?

Information Fetching and Solution Steps

• A hotel chargers $225 per night to rent a suite.
• The hotel also charges $75 per day for full room service.
• Jessica and Ashely purchased full room service for every night.
• They stayed at the hotel and spent a total of $1,200

As the total amount they spent = $1,200

As $75 is the service charges as Jessica and Ashely purchased full room service for every night.

Per night charges = hotel chargers + service charges

Per night charges = $225 + $75 ⇒ $300

So, total nights will be calculated as:

Total nights = total amount they spent ÷ Per night charges

Total nights = $1,200 ÷ $300 ⇒ 4 nights

Therefore, they spent 4 nights at the hotel. Hence, option B is correct.

                                 Question # 4 Solution

Answer:

Hence, |h − 57.5| ≤ 7.5 is the absolute values which best represents this restriction, where ( h ) represents height. Hence, option A is correct.

Information Fetching and Solution Steps

• A certain ride at an amusement park requires that children be at least 50 inches tall but no more that 65 inches tall.

Let us take the equation of following absolute value:

|h − 57.5| ≤ 7.5

We know h − 57.5 ≤ and h − 57.5 ≥ −50

h − 57.5 ≤ 7.5         (Condition 1)

h − 57.5 + 57.5 ≤ 7.5 + 57.5      (Add 57.5 to both sides)

h ≤ 65

h − 57.5 ≥ −7.5         (Condition 2)

h − 57.5 + 57.5 ≥ −7.5 + 57.5     (Add 57.5 to both sides)

h ≥ 50

So, h ≤ 65 and h ≥ 50

Solution Graph is also attached as shown in attached figure a.

Hence, |h − 57.5| ≤ 7.5 is the absolute values which best represents this restriction, where ( h ) represents height. Hence, option A is correct.

Using same methodology we observe that all other options B, C, and D brings wrong values which is as follows:

• |h+7.5|≤65 brings h≤57.5 and h≥−72.5
• |h+50|≤65 brings h≤15 and h≥−115
• |h+65|≤50 brings h≤−15 and h≥−115

Hence, from all discussion, we conclude that |h − 57.5| ≤ 7.5 is the absolute values which best represents this restriction, where ( h ) represents height, as it brings h ≤ 65 and h ≥ 50. Hence, option A is correct.

Keywords: inequality, graph solution, absolute value

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