8th Grade Algebra Word Problems Worksheet - Fill Online, Printable ... - Free Printable

Let's solve each problem step by step.

---

Problem 1:

Question: Your sister Samantha is turning 48 in April. She is 3 times older than your brother John, and twice as old as you. How old is your brother John?

Solution:
1. Let Samantha's age be \( S \). According to the problem, \( S = 48 \).
2. Samantha is 3 times older than John. Let John's age be \( J \). Therefore:
\[
S = 3J
\]
Substituting \( S = 48 \):
\[
48 = 3J
\]
3. Solve for \( J \):
\[
J = \frac{48}{3} = 16
\]

Answer: John is 16 years old.

---

Problem 2:

Question: Every seat that is sold in the auditorium costs $6. In addition to that, the auditorium makes $300 dollars as a flat rate. If the auditorium made $2772.00, how many seats were sold?

Solution:
1. Let the number of seats sold be \( x \).
2. The total revenue from selling seats is \( 6x \) (since each seat costs $6).
3. The auditorium also earns a flat rate of $300.
4. The total revenue is given as $2772. Therefore:
\[
6x + 300 = 2772
\]
5. Solve for \( x \):
\[
6x = 2772 - 300
\]
\[
6x = 2472
\]
\[
x = \frac{2472}{6} = 412
\]

Answer: The number of seats sold is 412.

---

Problem 3:

Question: John buys 6 shirts. For every shirt you purchase, you get one for 30% off. If the normal price for each shirt is $20.00, how much money did John spend on his shopping trip?

Solution:
1. John buys 6 shirts. For every shirt he buys, he gets another shirt at 30% off.
2. This means for every 2 shirts, he pays full price for 1 shirt and gets the second shirt at 30% off.
3. Calculate the cost for 2 shirts:
- Full price for 1 shirt: $20
- Discounted price for the second shirt: \( 20 \times (1 - 0.30) = 20 \times 0.70 = 14 \)
- Total cost for 2 shirts: \( 20 + 14 = 34 \)
4. Since John buys 6 shirts, he gets 3 pairs of shirts (each pair consisting of 2 shirts).
5. Total cost for 6 shirts:
\[
3 \times 34 = 102
\]

Answer: John spent $102 on his shopping trip.

---

Problem 4:

Question: Cassandra was drawing a circle. The radius of the circle turned out to be 4 cm long. How long was the circumference of the circle?

Solution:
1. The formula for the circumference \( C \) of a circle is:
\[
C = 2\pi r
\]
where \( r \) is the radius.
2. Given \( r = 4 \) cm:
\[
C = 2\pi \times 4 = 8\pi
\]
3. Using \( \pi \approx 3.14 \):
\[
C \approx 8 \times 3.14 = 25.12 \text{ cm}
\]

Answer: The circumference of the circle is \( 8\pi \) cm or approximately 25.12 cm.

---

Problem 5:

Question: American Airlines had a flight going out later that day. They charge $53 dollars for each first class ticket and $21 dollars for each coach ticket. There were 139 passengers total. 30% of the passengers composed the first class. How much money did American Airlines make total?

Solution:
1. Total number of passengers: \( 139 \).
2. Percentage of first-class passengers: 30%. Therefore, the number of first-class passengers is:
\[
0.30 \times 139 = 41.7 \approx 42 \text{ (rounding to the nearest whole number)}
\]
3. Number of coach passengers:
\[
139 - 42 = 97
\]
4. Revenue from first-class tickets:
\[
42 \times 53 = 2226 \text{ dollars}
\]
5. Revenue from coach tickets:
\[
97 \times 21 = 2037 \text{ dollars}
\]
6. Total revenue:
\[
2226 + 2037 = 4263 \text{ dollars}
\]

Answer: American Airlines made a total of $4263.

---

Final Answers:

1. John is 16 years old.
2. The number of seats sold is 412.
3. John spent $102.
4. The circumference of the circle is \( 8\pi \) cm or approximately 25.12 cm.
5. American Airlines made $4263.

\[
\boxed{16, 412, 102, 8\pi \text{ or } 25.12, 4263}
\]