Question

NEED HELP RIGHT AWAY DONT HAVE ANY TIME TO WAIT!!

1). Mrs. Charlton is giving you a test worth 100 points containing 40 problems. There are two-point problems and four-point problems on the test. How many of each problem are on the test? SHOW YOUR WORK FOR FULL CREDIT! Explain all steps in complete sentences.

2). Suppose you are starting an office-cleaning service. You have spent $315 on equipment. To clean an office, you use $4 worth of supplies. You charge $25 per office. How many offices must you clean to break even? SHOW YOUR WORK FOR FULL CREDIT! Explain all steps in complete sentences.

3). A light plane flew from its home base to an airport 255 miles away. With the head wind, the trip took 1.7 hours. The return trip with a tail wind took 1.5 hours. Find the average airspeed of the plane and the average wind speed. SHOW YOUR WORK FOR FULL CREDIT! Explain all steps in complete sentences.

Answer 1

Answer: There are 10 4-marks questions and 30 2-marks questions.

Answer 2

Question 1:
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Total points = 100
Total question = 40
Type of questions : 2-points question and 4-points questions

Assumed all 40 questions are 2-points questions.
Total points = 40 x 2 = 80

Difference in points = 100 - 80 = 20 points
Difference in the 2 type of questions = 4 - 2 = 2

Number of 4 marks questions = 20 ÷ 2 = 10

Number of 2 marks questions = 40 - 10 = 30

Answer: There are 10 4-marks questions and 30 2-marks questions.

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Question 2:
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Let x be the number of offices you need to clean.

Total cost = 315 + 4x
Total revenue = 25x

To break even,
315 + 4x = 25x
21x = 315
x = 15

Answer: You need to clean 15 offices to break even.

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Question 3:
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Total distance (including return trip) = 255 + 255 = 510 miles

Total time taken = 1.7 + 1.5 = 3.2 hours

Speed = Distance ÷ time

Speed = 510 ÷ 3.2 = 159.38 miles/hour

Answer: The average speed is 159.38 miles/hour