High School

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1. Twenty less than four times a certain number is 4. Determine the number.

A. 6
B. 5
C. 4
D. 3

2. What is the number of horsepower required to lift 10,000 gallons of water per hour to a height of 90 ft? Assume the weight of water is 8.5 lbs per gallon.

A. 3.56
B. 3.86
C. 4.86
D. 4.56

3. How many gallons of water can a 75 hp engine raise 150 ft in 5 hours? One gallon of water weighs 8.5 lbs.

A. 595,238 gallons
B. 594,238 gallons
C. 593,238 gallons
D. 594,328 gallons

4. One cubic foot of water is assumed to weigh 62.5 lbs. What is the weight of one cubic inch of water?

A. 0.0361 lbs
B. 0.0316 lbs
C. 0.0416 lbs
D. 0.0461 lbs

5. A man bought plumbing tools worth $2,100. The sales tax was 8%. How much did the man pay?

Answer :

Let's tackle each problem step-by-step.

  1. Determine the number:
    The problem states, "Twenty less than four times a certain number is 4."
    Let's represent the unknown number as [tex]x[/tex].

    The equation based on the problem is:

    [tex]4x - 20 = 4[/tex]

    To find [tex]x[/tex], we'll solve this equation:

    • Add 20 to both sides:
      [tex]4x - 20 + 20 = 4 + 20[/tex]
      [tex]4x = 24[/tex]

    • Divide both sides by 4:
      [tex]x = \frac{24}{4}[/tex]
      [tex]x = 6[/tex]

    Therefore, the number is A. 6.

  2. Number of horsepower to lift water:
    We need to calculate the horsepower required to lift 10,000 gallons of water per hour to a height of 90 ft. The weight of water is 8.5 lbs per gallon.

    First, calculate the total weight:
    [tex]10,000 \text{ gallons} \times 8.5 \text{ lbs/gallon} = 85,000 \text{ lbs}[/tex]

    The work done in lifting the water is:
    [tex]85,000 \text{ lbs} \times 90 \text{ ft} = 7,650,000 \text{ ft-lbs}[/tex]

    Since 1 horsepower equals 550 ft-lbs per second, convert to horsepower:

    [tex]\text{Horsepower} = \frac{7,650,000}{550 \times 3600} \approx 3.86[/tex]

    Therefore, the horsepower required is B. 3.86.

  3. Gallons of water raised:
    We want to find out how many gallons a 75 hp engine can raise 150 ft in 5 hours.

    Work done by the engine in 5 hours:
    [tex]75 \text{ hp} \times 550 \text{ ft-lbs/sec} \times 3600 \text{ sec/hour} \times 5 \text{ hours} = 742,500,000 \text{ ft-lbs}[/tex]

    Weight of water raised:
    [tex]742,500,000 \div 150 \text{ ft} = 4,950,000 \text{ lbs}[/tex]

    Convert to gallons:
    [tex]\frac{4,950,000}{8.5} \approx 582,353 \text{ gallons}[/tex]

    Since there's likely a slight error in choices, the logical closest answer might be close but needs clear information to confirm.

  4. Weight of one cubic inch of water:

    Given: 1 cubic foot of water weighs 62.5 lbs. There are 1728 cubic inches in a cubic foot, so:

    [tex]\text{Weight per cubic inch} = \frac{62.5}{1728} \approx 0.0361 \text{ lbs/inch}^3[/tex]

    Therefore, the weight is A. 0.0361.

  5. Total cost with sales tax:

    Original cost of plumbing tools: $2100.

    Sales tax at 8% is:
    [tex]2100 \times 0.08 = 168[/tex]

    Total cost paid by the man:
    [tex]2100 + 168 = 2268[/tex]

    Therefore, the man paid a total of $2268.

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