Algebra 1 Worksheets | Word Problems Worksheets - Free Printable

Let's solve each problem step by step:

---

Problem 1:

The sum of three consecutive numbers is eighty-four. What is the smallest of the three numbers?

#### Solution:
Let the three consecutive numbers be \( x \), \( x+1 \), and \( x+2 \).

The sum of these numbers is:
\[
x + (x+1) + (x+2) = 84
\]

Simplify the equation:
\[
3x + 3 = 84
\]

Subtract 3 from both sides:
\[
3x = 81
\]

Divide by 3:
\[
x = 27
\]

Thus, the smallest number is:
\[
\boxed{27}
\]

---

Problem 2:

Tom sold half of his comic books and then bought six more. He now has twelve. How many did he begin with?

#### Solution:
Let the number of comic books Tom originally had be \( x \).

He sold half of them, so he had:
\[
x - \frac{x}{2} = \frac{x}{2}
\]

Then he bought six more, so he now has:
\[
\frac{x}{2} + 6 = 12
\]

Subtract 6 from both sides:
\[
\frac{x}{2} = 6
\]

Multiply both sides by 2:
\[
x = 12
\]

Thus, Tom began with:
\[
\boxed{12}
\]

---

Problem 3:

Oceanside Bike Rental Shop charges 14 dollars plus 9 dollars an hour for renting a bike. Joan paid 86 dollars to rent a bike. How many hours did she pay to have the bike checked out?

#### Solution:
The total cost of renting the bike is given by:
\[
\text{Total Cost} = 14 + 9 \times \text{Number of Hours}
\]

Let the number of hours be \( h \). The equation becomes:
\[
14 + 9h = 86
\]

Subtract 14 from both sides:
\[
9h = 72
\]

Divide by 9:
\[
h = 8
\]

Thus, Joan rented the bike for:
\[
\boxed{8}
\]

---

Problem 4:

The sum of three consecutive even numbers is 156. What is the smallest of the three numbers?

#### Solution:
Let the three consecutive even numbers be \( x \), \( x+2 \), and \( x+4 \).

The sum of these numbers is:
\[
x + (x+2) + (x+4) = 156
\]

Simplify the equation:
\[
3x + 6 = 156
\]

Subtract 6 from both sides:
\[
3x = 150
\]

Divide by 3:
\[
x = 50
\]

Thus, the smallest number is:
\[
\boxed{50}
\]

---

Problem 5:

The sum of three consecutive odd numbers is one hundred and eleven. What is the smallest of the three numbers?

#### Solution:
Let the three consecutive odd numbers be \( x \), \( x+2 \), and \( x+4 \).

The sum of these numbers is:
\[
x + (x+2) + (x+4) = 111
\]

Simplify the equation:
\[
3x + 6 = 111
\]

Subtract 6 from both sides:
\[
3x = 105
\]

Divide by 3:
\[
x = 35
\]

Thus, the smallest number is:
\[
\boxed{35}
\]

---

Problem 6:

On Monday, 301 students went on a trip to the zoo. All 7 buses were filled and 7 students had to travel in cars. How many students were in each bus?

#### Solution:
The total number of students who traveled by bus is:
\[
301 - 7 = 294
\]

Since all 7 buses were filled, the number of students per bus is:
\[
\frac{294}{7} = 42
\]

Thus, there were:
\[
\boxed{42}
\]
students in each bus.

---

Problem 7:

Mike bought four new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only twenty-nine cards left. How many cards did Mike start with?

#### Solution:
Let the number of cards Mike originally had be \( x \).

After buying 4 new cards, he had:
\[
x + 4
\]

The next day, his dog ate half of his collection, leaving him with:
\[
\frac{x + 4}{2} = 29
\]

Multiply both sides by 2:
\[
x + 4 = 58
\]

Subtract 4 from both sides:
\[
x = 54
\]

Thus, Mike started with:
\[
\boxed{54}
\]

---

Problem 8:

Sara had 207 dollars to spend on 9 books. After buying them, she had 18 dollars. How much did each book cost?

#### Solution:
The total amount Sara spent on the books is:
\[
207 - 18 = 189
\]

Since she bought 9 books, the cost of each book is:
\[
\frac{189}{9} = 21
\]

Thus, each book cost:
\[
\boxed{21}
\]

---

Problem 9:

Benny spent half of his allowance going to the movies. He washed the family car and earned 8 dollars. He ended with 16 dollars. What is his weekly allowance?

#### Solution:
Let Benny's weekly allowance be \( x \).

He spent half of it on movies, so he had:
\[
x - \frac{x}{2} = \frac{x}{2}
\]

After washing the car, he earned 8 dollars, so he had:
\[
\frac{x}{2} + 8 = 16
\]

Subtract 8 from both sides:
\[
\frac{x}{2} = 8
\]

Multiply both sides by 2:
\[
x = 16
\]

Thus, Benny's weekly allowance is:
\[
\boxed{16}
\]

---

Problem 10:

Sandy bought a soft drink for two dollars and five candy bars. She spent a total of seventeen dollars. How much did each candy bar cost?

#### Solution:
Let the cost of each candy bar be \( y \).

The total cost of the soft drink and the candy bars is:
\[
2 + 5y = 17
\]

Subtract 2 from both sides:
\[
5y = 15
\]

Divide by 5:
\[
y = 3
\]

Thus, each candy bar cost:
\[
\boxed{3}
\]

---

Final Answers:

1. \(\boxed{27}\)
2. \(\boxed{12}\)
3. \(\boxed{8}\)
4. \(\boxed{50}\)
5. \(\boxed{35}\)
6. \(\boxed{42}\)
7. \(\boxed{54}\)
8. \(\boxed{21}\)
9. \(\boxed{16}\)
10. \(\boxed{3}\)