One Variable Word Problems Practice 2 worksheet featuring eight algebraic word problems for students to solve.
A worksheet titled "One Variable Word Problems Practice 2" with eight word problems involving algebraic equations, designed for students to write and solve equations based on given scenarios.
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Step-by-step solution for: One Variable Word Problems Notes and Worksheets - Lindsay Bowden
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Show Answer Key & Explanations
Step-by-step solution for: One Variable Word Problems Notes and Worksheets - Lindsay Bowden
Here are the step-by-step solutions for each problem on the worksheet.
1. Lily has 3 less than 4 times the amount of t-shirts as Bree. If Bree has 33 t-shirts, how many does Lily have?
* Step 1: Identify the variable. Let $L$ be the number of t-shirts Lily has. We know Bree has 33.
* Step 2: Write the equation. "4 times Bree's amount" is $4 \times 33$. "3 less than" that means we subtract 3.
Equation: $L = (4 \times 33) - 3$
* Step 3: Solve.
$4 \times 33 = 132$
$132 - 3 = 129$
* Answer: Lily has 129 t-shirts.
2. 4 times a number is equivalent to 8 more than 2 times the number. What is the number?
* Step 1: Let $x$ be the number.
* Step 2: Write the equation. "4 times a number" is $4x$. "8 more than 2 times the number" is $2x + 8$. Since they are equivalent (equal):
Equation: $4x = 2x + 8$
* Step 3: Solve for $x$. Subtract $2x$ from both sides.
$2x = 8$
Divide by 2:
$x = 4$
* Answer: The number is 4.
3. Pedro is 8 years older than twice the age of his cousin. If Pedro is 30, how old is his cousin?
* Step 1: Let $c$ be the cousin's age. Pedro is 30.
* Step 2: Write the equation. "Twice the age of his cousin" is $2c$. "8 years older" means add 8.
Equation: $30 = 2c + 8$
* Step 3: Solve for $c$. Subtract 8 from both sides.
$22 = 2c$
Divide by 2:
$11 = c$
* Answer: His cousin is 11 years old.
4. A car rental service charges a rental fee of $\$125$ plus $\$30$ per hour to rent a car. If Craig’s total bill is $\$305$, how many hours did he have the rental car?
* Step 1: Let $h$ be the number of hours.
* Step 2: Write the equation. The cost is $\$30$ times hours ($30h$) plus the flat fee ($\$125$). The total is $\$305$.
Equation: $30h + 125 = 305$
* Step 3: Solve for $h$. Subtract 125 from both sides.
$30h = 180$
Divide by 30:
$h = 6$
* Answer: He had the car for 6 hours.
5. 2 times a number increased by 10 is 24. Find the number.
* Step 1: Let $n$ be the number.
* Step 2: Write the equation. "2 times a number" is $2n$. "Increased by 10" means add 10. The result is 24.
Equation: $2n + 10 = 24$
* Step 3: Solve for $n$. Subtract 10 from both sides.
$2n = 14$
Divide by 2:
$n = 7$
* Answer: The number is 7.
6. Kyla spent 120 minutes reading this week. If this was 10 more than 2 times the amount of time she spent reading last week, how many minutes did she read last week?
* Step 1: Let $m$ be the minutes read last week. This week she read 120 minutes.
* Step 2: Write the equation. "2 times last week" is $2m$. "10 more than" that is $2m + 10$. This equals this week's time (120).
Equation: $2m + 10 = 120$
* Step 3: Solve for $m$. Subtract 10 from both sides.
$2m = 110$
Divide by 2:
$m = 55$
* Answer: She read 55 minutes last week.
7. The sum of 3 consecutive even numbers is 18. What are the three numbers?
* Step 1: Define the variables. Consecutive even numbers go up by 2 (like 2, 4, 6). Let the first number be $x$. The next is $x+2$. The third is $x+4$.
* Step 2: Write the equation. Their sum is 18.
Equation: $x + (x + 2) + (x + 4) = 18$
* Step 3: Solve for $x$. Combine like terms ($x+x+x = 3x$ and $2+4=6$).
$3x + 6 = 18$
Subtract 6 from both sides:
$3x = 12$
Divide by 3:
$x = 4$
* Step 4: Find all three numbers.
First number ($x$) = 4
Second number ($x+2$) = 6
Third number ($x+4$) = 8
* Answer: The numbers are 4, 6, and 8.
8. You give a third of your weekly allowance to a charity. Then you spend $\$8$ at the mall. If you have $\$2$ left to spend, how much is your weekly allowance?
* Step 1: Let $a$ be the total allowance.
* Step 2: Write the equation. You start with $a$. You give away $\frac{1}{3}a$ (so you keep $\frac{2}{3}a$, or simply subtract $\frac{1}{3}a$). Then subtract $\$8$. You have $\$2$ left.
Equation: $a - \frac{1}{3}a - 8 = 2$
*(Alternatively, think of it as: The money kept minus spending equals remaining. $\frac{2}{3}a - 8 = 2$)*
* Step 3: Solve for $a$. Add 8 to both sides.
$\frac{2}{3}a = 10$
To isolate $a$, multiply both sides by $\frac{3}{2}$ (or divide by 2 then multiply by 3).
$10 / 2 = 5$
$5 \times 3 = 15$
$a = 15$
* Check: Allowance is $\$15$. One third is $\$5$. $15 - 5 = 10$. Spend $\$8$. $10 - 8 = 2$. Correct.
* Answer: Your weekly allowance is $\$15$.
Final Answer:
1. 129 t-shirts
2. 4
3. 11 years old
4. 6 hours
5. 7
6. 55 minutes
7. 4, 6, and 8
8. $15
1. Lily has 3 less than 4 times the amount of t-shirts as Bree. If Bree has 33 t-shirts, how many does Lily have?
* Step 1: Identify the variable. Let $L$ be the number of t-shirts Lily has. We know Bree has 33.
* Step 2: Write the equation. "4 times Bree's amount" is $4 \times 33$. "3 less than" that means we subtract 3.
Equation: $L = (4 \times 33) - 3$
* Step 3: Solve.
$4 \times 33 = 132$
$132 - 3 = 129$
* Answer: Lily has 129 t-shirts.
2. 4 times a number is equivalent to 8 more than 2 times the number. What is the number?
* Step 1: Let $x$ be the number.
* Step 2: Write the equation. "4 times a number" is $4x$. "8 more than 2 times the number" is $2x + 8$. Since they are equivalent (equal):
Equation: $4x = 2x + 8$
* Step 3: Solve for $x$. Subtract $2x$ from both sides.
$2x = 8$
Divide by 2:
$x = 4$
* Answer: The number is 4.
3. Pedro is 8 years older than twice the age of his cousin. If Pedro is 30, how old is his cousin?
* Step 1: Let $c$ be the cousin's age. Pedro is 30.
* Step 2: Write the equation. "Twice the age of his cousin" is $2c$. "8 years older" means add 8.
Equation: $30 = 2c + 8$
* Step 3: Solve for $c$. Subtract 8 from both sides.
$22 = 2c$
Divide by 2:
$11 = c$
* Answer: His cousin is 11 years old.
4. A car rental service charges a rental fee of $\$125$ plus $\$30$ per hour to rent a car. If Craig’s total bill is $\$305$, how many hours did he have the rental car?
* Step 1: Let $h$ be the number of hours.
* Step 2: Write the equation. The cost is $\$30$ times hours ($30h$) plus the flat fee ($\$125$). The total is $\$305$.
Equation: $30h + 125 = 305$
* Step 3: Solve for $h$. Subtract 125 from both sides.
$30h = 180$
Divide by 30:
$h = 6$
* Answer: He had the car for 6 hours.
5. 2 times a number increased by 10 is 24. Find the number.
* Step 1: Let $n$ be the number.
* Step 2: Write the equation. "2 times a number" is $2n$. "Increased by 10" means add 10. The result is 24.
Equation: $2n + 10 = 24$
* Step 3: Solve for $n$. Subtract 10 from both sides.
$2n = 14$
Divide by 2:
$n = 7$
* Answer: The number is 7.
6. Kyla spent 120 minutes reading this week. If this was 10 more than 2 times the amount of time she spent reading last week, how many minutes did she read last week?
* Step 1: Let $m$ be the minutes read last week. This week she read 120 minutes.
* Step 2: Write the equation. "2 times last week" is $2m$. "10 more than" that is $2m + 10$. This equals this week's time (120).
Equation: $2m + 10 = 120$
* Step 3: Solve for $m$. Subtract 10 from both sides.
$2m = 110$
Divide by 2:
$m = 55$
* Answer: She read 55 minutes last week.
7. The sum of 3 consecutive even numbers is 18. What are the three numbers?
* Step 1: Define the variables. Consecutive even numbers go up by 2 (like 2, 4, 6). Let the first number be $x$. The next is $x+2$. The third is $x+4$.
* Step 2: Write the equation. Their sum is 18.
Equation: $x + (x + 2) + (x + 4) = 18$
* Step 3: Solve for $x$. Combine like terms ($x+x+x = 3x$ and $2+4=6$).
$3x + 6 = 18$
Subtract 6 from both sides:
$3x = 12$
Divide by 3:
$x = 4$
* Step 4: Find all three numbers.
First number ($x$) = 4
Second number ($x+2$) = 6
Third number ($x+4$) = 8
* Answer: The numbers are 4, 6, and 8.
8. You give a third of your weekly allowance to a charity. Then you spend $\$8$ at the mall. If you have $\$2$ left to spend, how much is your weekly allowance?
* Step 1: Let $a$ be the total allowance.
* Step 2: Write the equation. You start with $a$. You give away $\frac{1}{3}a$ (so you keep $\frac{2}{3}a$, or simply subtract $\frac{1}{3}a$). Then subtract $\$8$. You have $\$2$ left.
Equation: $a - \frac{1}{3}a - 8 = 2$
*(Alternatively, think of it as: The money kept minus spending equals remaining. $\frac{2}{3}a - 8 = 2$)*
* Step 3: Solve for $a$. Add 8 to both sides.
$\frac{2}{3}a = 10$
To isolate $a$, multiply both sides by $\frac{3}{2}$ (or divide by 2 then multiply by 3).
$10 / 2 = 5$
$5 \times 3 = 15$
$a = 15$
* Check: Allowance is $\$15$. One third is $\$5$. $15 - 5 = 10$. Spend $\$8$. $10 - 8 = 2$. Correct.
* Answer: Your weekly allowance is $\$15$.
Final Answer:
1. 129 t-shirts
2. 4
3. 11 years old
4. 6 hours
5. 7
6. 55 minutes
7. 4, 6, and 8
8. $15
Parent Tip: Review the logic above to help your child master the concept of basic algebra word problems worksheet.
