Math word problems worksheet with ten questions on consecutive numbers, money, and basic operations.
A math worksheet titled "Word Problems" with ten questions involving basic arithmetic and algebra, including consecutive numbers, money calculations, and division. The worksheet has spaces for the student's name, teacher, score, and date, and is from Math-Aids.Com.
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Show Answer Key & Explanations
Step-by-step solution for: Algebra 1 Worksheets | Word Problems Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Algebra 1 Worksheets | Word Problems Worksheets
Here are the step-by-step solutions for each word problem on the worksheet.
1) The sum of three consecutive numbers is eighty-four. What is the smallest of the three numbers?
* Step 1: Let the smallest number be $x$. Since they are consecutive, the next two numbers are $x + 1$ and $x + 2$.
* Step 2: Write the equation: $x + (x + 1) + (x + 2) = 84$.
* Step 3: Combine like terms: $3x + 3 = 84$.
* Step 4: Subtract 3 from both sides: $3x = 81$.
* Step 5: Divide by 3: $x = 27$.
* Check: $27 + 28 + 29 = 84$. Correct.
2) Tom sold half of his comic books and then bought six more. He now has twelve. How many did he begin with?
* Step 1: Work backward from the end. He ended with 12 comics.
* Step 2: Before that, he bought 6 more. So, subtract those 6 to see how many he had before buying: $12 - 6 = 6$.
* Step 3: Before that, he sold half of his collection. This means the 6 he had left were the other half. To find the starting amount, multiply by 2: $6 \times 2 = 12$.
* Check: Start with 12. Sell half (6). You have 6 left. Buy 6 more. You have 12. Correct.
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?
* Step 1: Identify the fixed cost ($14) and the hourly cost ($9). Total paid is $86.
* Step 2: Subtract the fixed cost from the total to find the cost just for the hours: $86 - 14 = 72$.
* Step 3: Divide the remaining amount by the hourly rate to find the number of hours: $72 / 9 = 8$.
4) The sum of three consecutive even numbers is 156. What is the smallest of the three numbers?
* Step 1: Let the smallest even number be $x$. The next consecutive even numbers are $x + 2$ and $x + 4$.
* Step 2: Write the equation: $x + (x + 2) + (x + 4) = 156$.
* Step 3: Combine like terms: $3x + 6 = 156$.
* Step 4: Subtract 6 from both sides: $3x = 150$.
* Step 5: Divide by 3: $x = 50$.
* Check: $50 + 52 + 54 = 156$. Correct.
5) The sum of three consecutive odd numbers is one hundred and eleven. What is the smallest of the three numbers?
* Step 1: Let the smallest odd number be $x$. The next consecutive odd numbers are $x + 2$ and $x + 4$.
* Step 2: Write the equation: $x + (x + 2) + (x + 4) = 111$.
* Step 3: Combine like terms: $3x + 6 = 111$.
* Step 4: Subtract 6 from both sides: $3x = 105$.
* Step 5: Divide by 3: $x = 35$.
* Check: $35 + 37 + 39 = 111$. Correct.
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?
* Step 1: Subtract the students who traveled in cars from the total number of students to find how many rode the buses: $301 - 7 = 294$.
* Step 2: Divide the number of bus riders by the number of buses: $294 / 7$.
* Calculation: $294 / 7 = 42$.
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?
* Step 1: Work backward. He has 29 cards left.
* Step 2: Before the dog ate half, he must have had twice as many. $29 \times 2 = 58$.
* Step 3: Before he bought the 4 new cards, he had 4 fewer. $58 - 4 = 54$.
8) Sara had 207 dollars to spend on 9 books. After buying them she had 18 dollars. How much did each book cost?
* Step 1: Find out how much money she actually spent by subtracting what she had left from what she started with: $207 - 18 = 189$.
* Step 2: Divide the total amount spent by the number of books to find the cost per book: $189 / 9$.
* Calculation: $189 / 9 = 21$.
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?
* Step 1: Work backward. He ended with $16.
* Step 2: Subtract the $8 he earned washing the car to see how much he had before that: $16 - 8 = 8$.
* Step 3: This $8 represents the half of his allowance he had left after spending half at the movies. To find the full allowance, multiply by 2: $8 \times 2 = 16$.
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?
* Step 1: Subtract the cost of the soft drink from the total spent to find the cost of just the candy bars: $17 - 2 = 15$.
* Step 2: Divide the remaining amount by the number of candy bars (5) to find the cost of one: $15 / 5 = 3$.
Final Answer:
1) 27
2) 12
3) 8
4) 50
5) 35
6) 42
7) 54
8) 21
9) 16
10) 3
1) The sum of three consecutive numbers is eighty-four. What is the smallest of the three numbers?
* Step 1: Let the smallest number be $x$. Since they are consecutive, the next two numbers are $x + 1$ and $x + 2$.
* Step 2: Write the equation: $x + (x + 1) + (x + 2) = 84$.
* Step 3: Combine like terms: $3x + 3 = 84$.
* Step 4: Subtract 3 from both sides: $3x = 81$.
* Step 5: Divide by 3: $x = 27$.
* Check: $27 + 28 + 29 = 84$. Correct.
2) Tom sold half of his comic books and then bought six more. He now has twelve. How many did he begin with?
* Step 1: Work backward from the end. He ended with 12 comics.
* Step 2: Before that, he bought 6 more. So, subtract those 6 to see how many he had before buying: $12 - 6 = 6$.
* Step 3: Before that, he sold half of his collection. This means the 6 he had left were the other half. To find the starting amount, multiply by 2: $6 \times 2 = 12$.
* Check: Start with 12. Sell half (6). You have 6 left. Buy 6 more. You have 12. Correct.
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?
* Step 1: Identify the fixed cost ($14) and the hourly cost ($9). Total paid is $86.
* Step 2: Subtract the fixed cost from the total to find the cost just for the hours: $86 - 14 = 72$.
* Step 3: Divide the remaining amount by the hourly rate to find the number of hours: $72 / 9 = 8$.
4) The sum of three consecutive even numbers is 156. What is the smallest of the three numbers?
* Step 1: Let the smallest even number be $x$. The next consecutive even numbers are $x + 2$ and $x + 4$.
* Step 2: Write the equation: $x + (x + 2) + (x + 4) = 156$.
* Step 3: Combine like terms: $3x + 6 = 156$.
* Step 4: Subtract 6 from both sides: $3x = 150$.
* Step 5: Divide by 3: $x = 50$.
* Check: $50 + 52 + 54 = 156$. Correct.
5) The sum of three consecutive odd numbers is one hundred and eleven. What is the smallest of the three numbers?
* Step 1: Let the smallest odd number be $x$. The next consecutive odd numbers are $x + 2$ and $x + 4$.
* Step 2: Write the equation: $x + (x + 2) + (x + 4) = 111$.
* Step 3: Combine like terms: $3x + 6 = 111$.
* Step 4: Subtract 6 from both sides: $3x = 105$.
* Step 5: Divide by 3: $x = 35$.
* Check: $35 + 37 + 39 = 111$. Correct.
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?
* Step 1: Subtract the students who traveled in cars from the total number of students to find how many rode the buses: $301 - 7 = 294$.
* Step 2: Divide the number of bus riders by the number of buses: $294 / 7$.
* Calculation: $294 / 7 = 42$.
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?
* Step 1: Work backward. He has 29 cards left.
* Step 2: Before the dog ate half, he must have had twice as many. $29 \times 2 = 58$.
* Step 3: Before he bought the 4 new cards, he had 4 fewer. $58 - 4 = 54$.
8) Sara had 207 dollars to spend on 9 books. After buying them she had 18 dollars. How much did each book cost?
* Step 1: Find out how much money she actually spent by subtracting what she had left from what she started with: $207 - 18 = 189$.
* Step 2: Divide the total amount spent by the number of books to find the cost per book: $189 / 9$.
* Calculation: $189 / 9 = 21$.
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?
* Step 1: Work backward. He ended with $16.
* Step 2: Subtract the $8 he earned washing the car to see how much he had before that: $16 - 8 = 8$.
* Step 3: This $8 represents the half of his allowance he had left after spending half at the movies. To find the full allowance, multiply by 2: $8 \times 2 = 16$.
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?
* Step 1: Subtract the cost of the soft drink from the total spent to find the cost of just the candy bars: $17 - 2 = 15$.
* Step 2: Divide the remaining amount by the number of candy bars (5) to find the cost of one: $15 / 5 = 3$.
Final Answer:
1) 27
2) 12
3) 8
4) 50
5) 35
6) 42
7) 54
8) 21
9) 16
10) 3
Parent Tip: Review the logic above to help your child master the concept of pre algebra word problem worksheet.
