Let's solve each of the
one-variable word problems step-by-step using the method outlined:
1.
Determine the variable
2.
Set up the equation
3.
Solve
---
Problem 1:
"8 less than 3 times a number is 13. Find the number."
-
Step 1: Determine the variable
Let $ x $ = the number
-
Step 2: Set up the equation
"3 times a number" → $ 3x $
"8 less than" → $ 3x - 8 $
"is 13" → $ = 13 $
So, the equation is:
$$
3x - 8 = 13
$$
-
Step 3: Solve
$$
3x - 8 = 13 \\
3x = 13 + 8 \\
3x = 21 \\
x = \frac{21}{3} = 7
$$
✔ Answer: The number is
7
---
Problem 2:
"Amy scores 7 points more than 2 times Jill on their unit test. If Amy scored an 87, what did Jill score?"
-
Step 1: Determine the variable
Let $ j $ = Jill’s score
-
Step 2: Set up the equation
"2 times Jill" → $ 2j $
"7 more than" → $ 2j + 7 $
"Amy scored 87" → $ = 87 $
Equation:
$$
2j + 7 = 87
$$
-
Step 3: Solve
$$
2j + 7 = 87 \\
2j = 87 - 7 = 80 \\
j = \frac{80}{2} = 40
$$
✔ Answer: Jill scored
40
---
Problem 3:
"Ava makes 7 dollars per hour plus a weekly bonus of $10. If her paycheck this week was $80, how many hours did she work?"
-
Step 1: Determine the variable
Let $ h $ = number of hours worked
-
Step 2: Set up the equation
Pay = hourly rate × hours + bonus
$$
7h + 10 = 80
$$
-
Step 3: Solve
$$
7h + 10 = 80 \\
7h = 70 \\
h = \frac{70}{7} = 10
$$
✔ Answer: Ava worked
10 hours
---
Problem 4:
"Emmanuel is 2 times older than Jaime. Their ages add to 54. Find both of their ages."
-
Step 1: Determine the variable
Let $ j $ = Jaime’s age
Then Emmanuel’s age = $ 2j $
-
Step 2: Set up the equation
Sum of their ages:
$$
j + 2j = 54
$$
-
Step 3: Solve
$$
3j = 54 \\
j = 18
$$
So, Jaime is 18, and Emmanuel is $ 2 \times 18 = 36 $
✔ Answer: Jaime is
18, Emmanuel is
36
---
Problem 5:
"Giselle paid an accountant $25 per hour to do her taxes plus a $100 one-time fee. Her total bill was $250. How many hours did the accountant work?"
-
Step 1: Determine the variable
Let $ h $ = number of hours worked
-
Step 2: Set up the equation
Total cost = hourly rate × hours + fixed fee
$$
25h + 100 = 250
$$
-
Step 3: Solve
$$
25h + 100 = 250 \\
25h = 150 \\
h = \frac{150}{25} = 6
$$
✔ Answer: The accountant worked
6 hours
---
Problem 6:
"9 more than a number divided by 8 is 10. What is the number?"
-
Step 1: Determine the variable
Let $ x $ = the number
-
Step 2: Set up the equation
"a number divided by 8" → $ \frac{x}{8} $
"9 more than" → $ \frac{x}{8} + 9 $
"is 10" → $ = 10 $
Equation:
$$
\frac{x}{8} + 9 = 10
$$
-
Step 3: Solve
$$
\frac{x}{8} + 9 = 10 \\
\frac{x}{8} = 1 \\
x = 8
$$
✔ Answer: The number is
8
---
✔ Final Answers Summary:
| Problem | Answer |
|--------|--------|
| 1 | 7 |
| 2 | Jill scored 40 |
| 3 | 10 hours |
| 4 | Jaime: 18, Emmanuel: 36 |
| 5 | 6 hours |
| 6 | 8 |
Let me know if you'd like these written out neatly for a worksheet!
Parent Tip: Review the logic above to help your child master the concept of using equations to solve word problems worksheet.
