# Week Four Assignment - Ch. 5 Cumulative Test Problems,Week 4

Week Four Assignment - Ch. 5 Cumulative Test Problems

5.1

22)

34)

46)

5.2

20)

36)

46)

5.3

28)

34)

42)

5.4

56)

60)

70)

5.5

32)

52)

70)

5.6

20) Science and medicine. A small business jet took 1 h longer to fly 810 mi on the

first part of a flight than to fly 540 mi on the second portion. If the jet's rate was the

same for each leg of the flight, what was the flying time for each leg?

30) Business and finance. If 342 cups of coffee can be made from 9 lb of coffee, how

many cups can be made from 6 lb of coffee?

36) Social science. A woman casts a 4 ft-shadow. At the same time, a 72-ft building

casts a 48 ft-shadow. How tall is the woman?

5.7

8)

30) Geometry. The area of the rectangle shown below is .. Find the width

Week 4 Checkpoint Chapter five

Section 5.5

Solve and check each of the following equations for x

24.

Solution:

Check:

48.

Solution:

Check:

56.

Solution:

Check:

Solve each of the following equations for x

72.

Solution:

Check:

Section 5.6 Solve the following word problems

6. Number problem. If one-half of one integer is subtracted from 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.

18. 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.

22. 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.

26. 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.

34. 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.

Section 5.7

Simplify each complex fraction

10.

Solution:

28.Fungicides account for 1/10 of the pesticides used in the

United States. Insecticides account for ¼ of all the pesticides used in the United States. The ratio of fungicides to insecticides used in the United States can be

write this ratio in simplest form

Solution:

32. simplify the formula

Solution:

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#### Solution Preview

Week Four Assignment - Ch. 5 Cumulative Test Problems

5.1

22)

= (-10/15)(a^3 /a)(b^2 / b^4)(c^3 /c)

= (-2/5)(a^2 c^2)/(b^2)

34)

= (3x - 2)(2x + 1)/(3x - 2)(x - 1)

= (2x + 1)/(x - 1)

46)

= (2x + 3)(2x + 3)/(2x + 3)

= 2x + 3

5.2

20)

= [a(a + b) * (2a - 3b)(2a + 3b)] / [(a + b)(2a - 3b) * a(5a - 4b)]

= (2a + 3b)/(5a - 4b)

36)

= [16x/{4(x - 2)(x + 2)}] / [4(x - 6)/{(x - 6)(x + 2)}]

= [4x/{(x - 2)(x + 2)}] * [(x + 2)/4]

= x/(x - 2)

46)

Please check and clarify if the first numerator and the second denominator are correct.

5.3

28)

= (y + 2 - 4y - 8)/3

= (-3y - 6)/3

= -3(y + 2)/3

= -y - 2

34)

= (3b - 8 + b - ...

#### Solution Summary

The rational expressions and simplifying fractions are determined. A complete, neat and step-by-step solutions are provided in the attached files.