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    Solving Equations and Word Problems

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    Solve and check each of the following equations for x

    1.

    2.

    3.

    Solve each of the following equations for x

    4.

    Solve the following word problems

    5. Number problem. If one-half of one integer is subtracted form three-fifths of the next consecutive integer the difference is 3. What are the two integers?

    6. A passenger train can travel 325mi in the same time a freight train takes to travel 200mi. If the speed of the passenger train is 25 mi/h faster than the speed of the freight train, fin the speed of each.

    7. Ariana took 2 h longer to drive 360mi on the first day of a trip than she took to drive 270 mi on the second day. If her speed was the same on both days, what was the driving time each day?

    8. A plane flies 720 mi against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 h, what is the plane's speed in still air?

    9. Kevin earned $165 interest for 1 year on an investment of $1500. At the same rate, what amount of interest would be earned by an investment of $2500?

    Simplify each complex fraction

    10.

    11. write this ratio in simplest form

    12. simplify the formula

    © BrainMass Inc. brainmass.com October 7, 2022, 6:57 pm ad1c9bdddf
    https://brainmass.com/math/fractions-and-percentages/solving-equations-word-problems-152700

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    SOLUTION This solution is FREE courtesy of BrainMass!

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    Solve and check each of the following equations for x

    1.
    Solution:

    Check:

    2.

    Solution:

    Check:

    3.
    Solution:

    Check:

    Solve each of the following equations for x

    4.
    Solution:

    Check:

    Solve the following word problems

    5. Number problem. If one-half of one integer is subtracted form three-fifths of the next consecutive integer the difference is 3. What are the two integers?

    Solution: Assuming the first integer is .
    Then, the equation to be solved is .

    The first integer is 24 and the next integer is 25.

    6. A passenger train can travel 325mi in the same time a freight train takes to travel 200mi. If the speed of the passenger train is 25 mi/h faster than the speed of the freight train, fin the speed of each.

    Solution: Assuming the speed of the freight train is .
    Then, the equation to be solved is .

    Then, the speed of the freight train is 40 mi/h and the passenger train is 65 mi/h.

    7. Ariana took 2 h longer to drive 360mi on the first day of a trip than she took to drive 270 mi on the second day. If her speed was the same on both days, what was the driving time each day?

    Solution: Assuming the speed of the driving time for the second day is .
    Then, the equation to be solved is .

    Then, on the first day the driving time is 8 h and the second day is 6 h.

    8. A plane flies 720 mi against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 h, what is the plane's speed in still air?

    Solution: Assuming the speed is .
    Then, the equation to be solved is .

    From the quadratic formula:

    The speed must be positive. Then, the speed is 150 mi/h.

    9. Kevin earned $165 interest for 1 year on an investment of $1500. At the same rate, what amount of interest would be earned by an investment of $2500?

    Solution: Assuming the earned interest by an investment of 2500 is .
    Then, the equation to be solved is .

    Kevin earned $275 interest if he invests $2500.

    Simplify each complex fraction

    10.

    Solution:

    11. write this ratio in simplest form
    Solution:

    12. simplify the formula

    Solution:

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com October 7, 2022, 6:57 pm ad1c9bdddf>
    https://brainmass.com/math/fractions-and-percentages/solving-equations-word-problems-152700

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