# Solving Equations and Word Problems

Please see the attached file for the fully formatted problems.

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

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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:

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