8th-Grade Math Word Problems Worksheets - Free Printable

Problem 1:

Question:
5 hockey pucks and 3 hockey sticks cost $23.
5 hockey pucks and 1 hockey stick cost $20.
How much does 1 hockey puck cost?

Solution:
Let the cost of 1 hockey puck be \( x \) dollars, and the cost of 1 hockey stick be \( y \) dollars.

From the problem, we have two equations:
1. \( 5x + 3y = 23 \)
2. \( 5x + y = 20 \)

We can solve these equations step by step.

#### Step 1: Subtract the second equation from the first.
\[
(5x + 3y) - (5x + y) = 23 - 20
\]
\[
5x + 3y - 5x - y = 3
\]
\[
2y = 3
\]
\[
y = \frac{3}{2} = 1.5
\]

#### Step 2: Substitute \( y = 1.5 \) into the second equation.
\[
5x + y = 20
\]
\[
5x + 1.5 = 20
\]
\[
5x = 20 - 1.5
\]
\[
5x = 18.5
\]
\[
x = \frac{18.5}{5} = 3.7
\]

Thus, the cost of 1 hockey puck is \( \boxed{3.7} \) dollars.

---

Problem 2:

Question:
This year, your brother Jack will be 2 years from being twice as old as his sister Jen. Three years ago, Jack was three times as old as Jen. If Jen is 16 years old now, how old is Jack?

Solution:
Let Jack's current age be \( J \) and Jen's current age be \( 16 \).

#### Step 1: Use the information about their ages three years ago.
Three years ago, Jack's age was \( J - 3 \) and Jen's age was \( 16 - 3 = 13 \). According to the problem:
\[
J - 3 = 3 \times 13
\]
\[
J - 3 = 39
\]
\[
J = 39 + 3
\]
\[
J = 42
\]

#### Step 2: Verify the condition for this year.
This year, Jack is 42 years old, and Jen is 16 years old. The problem states that Jack will be 2 years from being twice as old as Jen. Let's check:
\[
\text{Twice Jen's age} = 2 \times 16 = 32
\]
\[
\text{Jack's age in 2 years} = 42 + 2 = 44
\]
Since \( 44 \) is indeed 2 years more than \( 32 \), the condition is satisfied.

Thus, Jack is \( \boxed{42} \) years old.

---

Problem 3:

Question:
Parents donated fudge for the fund-raiser for your classroom. 40 pounds of chocolate fudge sold for $2.15 per pound, and vanilla fudge sold for $1.95 per pound. Your class raised $158.20. How many pounds of fudge were sold?

Solution:
Let \( x \) be the number of pounds of chocolate fudge sold, and \( y \) be the number of pounds of vanilla fudge sold.

From the problem, we know:
1. The total revenue from chocolate fudge is \( 2.15x \).
2. The total revenue from vanilla fudge is \( 1.95y \).
3. The total revenue is $158.20.

The equation for total revenue is:
\[
2.15x + 1.95y = 158.20
\]

We also know that 40 pounds of chocolate fudge were sold, so:
\[
x = 40
\]

#### Step 1: Substitute \( x = 40 \) into the revenue equation.
\[
2.15(40) + 1.95y = 158.20
\]
\[
86 + 1.95y = 158.20
\]
\[
1.95y = 158.20 - 86
\]
\[
1.95y = 72.20
\]
\[
y = \frac{72.20}{1.95}
\]
\[
y = 37
\]

#### Step 2: Calculate the total pounds of fudge sold.
\[
x + y = 40 + 37 = 77
\]

Thus, the total pounds of fudge sold is \( \boxed{77} \).

---

Problem 4:

Question:
One of your friends is heading north for a holiday and the other friend is heading south. Their destinations are 1029 miles apart, and one car is traveling at 45 miles per hour while the other car is traveling at 53 miles per hour. How many hours before the two cars pass each other?

Solution:
Let the time it takes for the two cars to meet be \( t \) hours.

#### Step 1: Determine the relative speed of the two cars.
Since the cars are moving towards each other, their relative speed is the sum of their individual speeds:
\[
45 + 53 = 98 \text{ miles per hour}
\]

#### Step 2: Use the formula for distance.
The total distance between the two cars is 1029 miles. The time \( t \) it takes for them to meet is given by:
\[
\text{Distance} = \text{Relative Speed} \times \text{Time}
\]
\[
1029 = 98t
\]
\[
t = \frac{1029}{98}
\]
\[
t = 10.5
\]

Thus, the two cars will pass each other in \( \boxed{10.5} \) hours.

---

Problem 5:

Question:
Dana needs 300 pickets for her colorful picket fence. She wants equal amounts of each of her selected colors. She selects 2 red, 3 green, 9 yellow, and 6 blue. How many more of each color does Dana need to buy? If the bulbs cost 25 cents and you get 20% off if you purchase 50 or more of the same color and 30% off if you purchase 60 or more of the same color, how much does Dana need to spend?

Solution:
#### Step 1: Determine the number of pickets needed for each color.
Dana needs 300 pickets in total, and she wants an equal amount of each color. She has selected 2 red, 3 green, 9 yellow, and 6 blue, which totals:
\[
2 + 3 + 9 + 6 = 20 \text{ colors}
\]
The number of pickets per color is:
\[
\frac{300}{20} = 15
\]

#### Step 2: Calculate how many more pickets Dana needs for each color.
- Red: She needs 15 pickets, and she already has 2. So, she needs:
\[
15 - 2 = 13 \text{ more red pickets}
\]
- Green: She needs 15 pickets, and she already has 3. So, she needs:
\[
15 - 3 = 12 \text{ more green pickets}
\]
- Yellow: She needs 15 pickets, and she already has 9. So, she needs:
\[
15 - 9 = 6 \text{ more yellow pickets}
\]
- Blue: She needs 15 pickets, and she already has 6. So, she needs:
\[
15 - 6 = 9 \text{ more blue pickets}
\]

#### Step 3: Calculate the cost of the pickets.
Each picket costs 25 cents. We need to apply the discounts based on the quantities purchased:
- Red: 13 pickets (no discount):
\[
13 \times 0.25 = 3.25 \text{ dollars}
\]
- Green: 12 pickets (no discount):
\[
12 \times 0.25 = 3.00 \text{ dollars}
\]
- Yellow: 6 pickets (no discount):
\[
6 \times 0.25 = 1.50 \text{ dollars}
\]
- Blue: 9 pickets (no discount):
\[
9 \times 0.25 = 2.25 \text{ dollars}
\]

#### Step 4: Sum the total cost.
\[
3.25 + 3.00 + 1.50 + 2.25 = 10.00 \text{ dollars}
\]

Thus, Dana needs to spend \( \boxed{10.00} \) dollars.

---

Final Answers:

1. \( \boxed{3.7} \)
2. \( \boxed{42} \)
3. \( \boxed{77} \)
4. \( \boxed{10.5} \)
5. \( \boxed{10.00} \)