Here are the step-by-step solutions for each problem on the worksheet.
1) Students on a field trip
*
Step 1: Find out how many students rode on the buses. There were 331 students total, and 7 traveled in cars. So, $331 - 7 = 324$ students were on the buses.
*
Step 2: Divide the bus students by the number of buses. There were 6 buses. $324 \div 6 = 54$.
*
Check: $54 \times 6 = 324$. $324 + 7 = 331$. Correct.
2) Cost of pencils
*
Step 1: Find out how much money was actually spent. Aliyah started with $\$24$ and had $\$10$ left. So, she spent $24 - 10 = \$14$.
*
Step 2: Divide the amount spent by the number of pencils. She bought 7 pencils. $14 \div 7 = 2$.
*
Check: $7 \text{ pencils} \times \$2 = \$14$. $\$24 - \$14 = \$10$ left. Correct.
3) Sum of three consecutive numbers
*
Step 1: Let the smallest number be $x$. The next two numbers are $x+1$ and $x+2$.
*
Step 2: Write the equation: $x + (x+1) + (x+2) = 72$.
*
Step 3: Combine like terms: $3x + 3 = 72$.
*
Step 4: Subtract 3 from both sides: $3x = 69$.
*
Step 5: Divide by 3: $x = 23$.
*
Check: The numbers are 23, 24, and 25. $23 + 24 + 25 = 72$. Correct.
4) Sum of three consecutive even numbers
*
Step 1: Let the smallest even number be $x$. The next even numbers are $x+2$ and $x+4$ (since they skip the odd numbers in between).
*
Step 2: Write the equation: $x + (x+2) + (x+4) = 48$.
*
Step 3: Combine like terms: $3x + 6 = 48$.
*
Step 4: Subtract 6 from both sides: $3x = 42$.
*
Step 5: Divide by 3: $x = 14$.
*
Check: The numbers are 14, 16, and 18. $14 + 16 + 18 = 48$. Correct.
5) Cost of erasers
*
Step 1: Subtract the cost of the magazine from the total spent. Total spent was $\$25$, magazine was $\$5$. So, $25 - 5 = \$20$ was spent on erasers.
*
Step 2: Divide the eraser cost by the number of erasers. You bought 4 erasers. $20 \div 4 = 5$.
*
Check: $4 \text{ erasers} \times \$5 = \$20$. $\$20 + \$5 \text{ (magazine)} = \$25$. Correct.
6) Maria's boxes
*
Step 1: Work backward. Maria has 22 boxes left. This is *half* of what she had before the fire. So, before the fire, she had $22 \times 2 = 44$ boxes.
*
Step 2: These 44 boxes are what remained after she bought 7 more a week prior. To find the starting amount, subtract those 7 new boxes. $44 - 7 = 37$.
*
Check: Start with 37. Buy 7 more $\rightarrow$ 44. Half are destroyed ($44 \div 2$) $\rightarrow$ 22 left. Correct.
7) Sunalee's friends
*
Step 1: Find out how many balls were given away. She started with 40 and has 8 left. So, $40 - 8 = 32$ balls were given away.
*
Step 2: Divide the given balls by the number given to each friend. She gave 2 to each friend. $32 \div 2 = 16$.
*
Check: 16 friends $\times$ 2 balls each = 32 balls. $40 - 32 = 8$ remaining. Correct.
8) Imani's allowance
*
Step 1: Work backward from the final amount. Imani ended with $\$12$. Before that, she earned $\$4$ washing the car. So, before washing the car, she had $12 - 4 = \$8$.
*
Step 2: This $\$8$ represents half of her allowance because she spent the other half on mini-golf. To find the full allowance, multiply by 2. $8 \times 2 = 16$.
*
Check: Allowance is $\$16$. Spend half ($\$8$) on golf. Left with $\$8$. Earn $\$4$ washing car. End with $\$12$. Correct.
Final Answer:
1) 54 students
2) $2
3) 23
4) 14
5) $5
6) 37 boxes
7) 16 friends
8) $16
Parent Tip: Review the logic above to help your child master the concept of 2 step equations word problems worksheet.
