Algebra: Word Problems {Algebra 1 Worksheet} {Algebra Word - Free Printable

Let’s go through each problem one by one, solving them step by step.

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Problem 1:
*The sum of three consecutive numbers is eighty-four. What is the smallest of the three numbers?*

Let the smallest number be x.
Then the next two consecutive numbers are x+1 and x+2.
Sum = x + (x+1) + (x+2) = 3x + 3
Set equal to 84:
3x + 3 = 84
Subtract 3: 3x = 81
Divide by 3: x = 27
✔ Smallest number is 27

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Problem 2:
*Tom sold half of his comic books and then bought six more. He now has twelve. How many did he begin with?*

Let original number be x.
He sold half → left with x/2
Then bought 6 → x/2 + 6 = 12
Subtract 6: x/2 = 6
Multiply by 2: x = 12
✔ He began with 12 comic books.

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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?*

Fixed cost: $14
Hourly rate: $9/hour
Total paid: $86
So, amount spent on hours = 86 - 14 = 72
Hours = 72 ÷ 9 = 8
✔ She rented the bike for 8 hours.

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Problem 4:
*The sum of three consecutive even numbers is 156. What is the smallest of the three numbers?*

Let smallest even number be x.
Next two: x+2, x+4
Sum: x + (x+2) + (x+4) = 3x + 6 = 156
3x = 150
x = 50
✔ Smallest number is 50

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Problem 5:
*The sum of three consecutive odd numbers is one hundred and eleven. What is the smallest of the three numbers?*

Let smallest odd number be x.
Next two: x+2, x+4
Sum: x + (x+2) + (x+4) = 3x + 6 = 111
3x = 105
x = 35
✔ Smallest number is 35

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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?*

Total students = 301
Students in cars = 7
So students in buses = 301 - 7 = 294
Number of buses = 7
Students per bus = 294 ÷ 7 = 42
✔ Each bus had 42 students.

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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?*

Let original number be x.
He added 4 → x + 4
Dog ate half → left with (x+4)/2 = 29
Multiply both sides by 2: x + 4 = 58
Subtract 4: x = 54
✔ Mike started with 54 cards.

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Problem 8:
*Sara had 207 dollars to spend on 9 books. After buying them she had 18 dollars. How much did each book cost?*

Amount spent = 207 - 18 = 189
Number of books = 9
Cost per book = 189 ÷ 9 = 21
✔ Each book cost $21.

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Problem 9:
*Benny spent half of his allowance going to the movies. He washed the family car and earned 8 dollars. What is his weekly allowance if he ended with 16 dollars?*

Let allowance be x.
Spent half → left with x/2
Earned 8 → x/2 + 8 = 16
Subtract 8: x/2 = 8
Multiply by 2: x = 16
✔ His weekly allowance was $16.

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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?*

Drink cost: $2
Total spent: $17
So candy bars cost: 17 - 2 = 15
Number of candy bars: 5
Cost per bar: 15 ÷ 5 = 3
✔ Each candy bar cost $3.

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Final Answer:
1) 27
2) 12
3) 8
4) 50
5) 35
6) 42
7) 54
8) 21
9) 16
10) 3