Comprehensive worksheet designed to test students' ability to translate real-world scenarios into mathematical equations and solutions.

Let's solve each of these word problems step by step.

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1. Excavation for a pool is being done in your backyard. It measures 42F × 29F × 8F. The dirt that is taken out will be put into trucks that hold 4.53F³. How many truckloads of dirt will be taken away?

Step 1: Calculate the volume of dirt to be removed.
The pool dimensions are:
- Length = 42 feet
- Width = 29 feet
- Depth = 8 feet

Volume = Length × Width × Depth
= 42 × 29 × 8
= 1176 × 8
= 9,408 cubic feet

Step 2: Divide total volume by the capacity of one truck.
Each truck holds 4.53 ft³.

Number of truckloads = Total volume ÷ Truck capacity
= 9,408 ÷ 4.53
≈ 2,075.73

Since you can't have a fraction of a truckload, and you need to remove all the dirt, round up to the next whole number.

✔ Answer: 2,076 truckloads

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2. A magazine ad states that 4 out of 7 doctors recommend Flash toothpaste. If 1400 doctors were surveyed, how many doctors recommended Flash toothpaste?

We're told that 4 out of 7 doctors recommend it.

So, the fraction is:
4/7 of 1400

Calculate:
(4/7) × 1400 = (4 × 1400) / 7 = 5600 / 7 = 800

✔ Answer: 800 doctors

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3. February 2, the temperature at 11 AM was 55°F. At 10 PM, it had dropped to 3°F. To find the number of degrees the temperature dropped, which equation could you use? Let x be the number of degrees the temperature changed.

Temperature change = Initial temp – Final temp
= 55°F – 3°F = 52°F drop

So, if x is the number of degrees changed, then:

x = 55 - 3
or
x = 55 - 3 → x = 52

✔ Answer: x = 55 - 3

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4. Write an equation for the following situation. Four times the number of coins in my pocket plus 5 more is 29.

Let c = number of coins

"Four times the number of coins" = 4c
"Plus 5 more" = +5
"Is 29" = = 29

So:

4c + 5 = 29

✔ Answer: 4c + 5 = 29

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5. What is the best buy for the following advertised sale on pop?
a) 8 cans for $4.88
b) 10 cans for $5.80
c) 12 cans for $7.20

To find the best buy, calculate the price per can for each option.

a) 8 cans for $4.88
Price per can = 4.88 ÷ 8 = $0.61

b) 10 cans for $5.80
Price per can = 5.80 ÷ 10 = $0.58

c) 12 cans for $7.20
Price per can = 7.20 ÷ 12 = $0.60

Now compare:
- a: $0.61
- b: $0.58 ← lowest
- c: $0.60

✔ Answer: Option b (10 cans for $5.80) is the best buy.

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6. A 7 feet long ladder is leaning against the building. The foot of the ladder is 2 feet from the base of the building. How far up the wall is the top of the ladder?

This is a right triangle problem.

- Ladder = hypotenuse = 7 ft
- Distance from wall = one leg = 2 ft
- Height up the wall = other leg = ? (let’s call it h)

Use the Pythagorean theorem:

a² + b² = c²
where c = 7, a = 2, b = h

So:

2² + h² = 7²
4 + h² = 49
h² = 49 - 4 = 45
h = √45 ≈ 6.708 feet

✔ Answer: Approximately 6.71 feet up the wall

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✔ Final Answers Summary:

1. 2,076 truckloads
2. 800 doctors
3. x = 55 - 3
4. 4c + 5 = 29
5. Option b (10 cans for $5.80)
6. Approximately 6.71 feet

Let me know if you'd like any visual explanation or further breakdown!