Let’s solve each problem one by one. I’ll write the equation first, then solve it step by step.
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Problem 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?
Let L = number of t-shirts Lily has.
Bree has 33 → so 4 times that is 4 × 33 = 132.
“3 less than” that → 132 - 3 = 129.
Equation:
L = 4×33 - 3
L = 132 - 3
L = 129
✔ Final Answer for #1:
129
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Problem 2:
4 times a number is equivalent to 8 more than 2 times the number. What is the number?
Let x = the number.
Equation:
4x = 2x + 8
Subtract 2x from both sides:
4x - 2x = 8
2x = 8
Divide both sides by 2:
x = 4
✔ Final Answer for #2:
4
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Problem 3:
Pedro is 8 years older than twice the age of his cousin. If Pedro is 30, how old is his cousin?
Let c = cousin’s age.
Twice cousin’s age = 2c
8 years older than that = 2c + 8
That equals Pedro’s age: 30
Equation:
2c + 8 = 30
Subtract 8 from both sides:
2c = 22
Divide by 2:
c = 11
✔ Final Answer for #3:
11
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Problem 4:
A car rental service charges $125 plus $30 per hour. Craig’s total bill is $305. How many hours did he rent the car?
Let h = number of hours.
Total cost = 125 + 30h = 305
Equation:
125 + 30h = 305
Subtract 125 from both sides:
30h = 180
Divide by 30:
h = 6
✔ Final Answer for #4:
6
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Problem 5:
2 times a number increased by 10 is 24. Find the number.
Let n = the number.
“2 times a number” = 2n
“increased by 10” = 2n + 10
That equals 24.
Equation:
2n + 10 = 24
Subtract 10:
2n = 14
Divide by 2:
n = 7
✔ Final Answer for #5:
7
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Problem 6:
Kyla spent 120 minutes reading this week. That was 10 more than 2 times last week’s time. How many minutes did she read last week?
Let m = minutes read last week.
This week = 2m + 10 = 120
Equation:
2m + 10 = 120
Subtract 10:
2m = 110
Divide by 2:
m = 55
✔ Final Answer for #6:
55
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Problem 7:
The sum of 3 consecutive even numbers is 18. What are the three numbers?
Consecutive even numbers go up by 2 (like 2, 4, 6 or 10, 12, 14).
Let the first even number be x.
Then next two are x+2 and x+4.
Sum: x + (x+2) + (x+4) = 18
Simplify:
3x + 6 = 18
Subtract 6:
3x = 12
Divide by 3:
x = 4
So the numbers are: 4, 6, 8
Check: 4 + 6 + 8 = 18
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✔ Final Answer for #7:
4, 6, 8
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Problem 8:
You give a third of your weekly allowance to charity. Then you spend $8 at the mall. You have $2 left. How much is your weekly allowance?
Let A = weekly allowance.
Give away 1/3 → you have 2/3 left.
Then spend $8 → now you have $2.
So:
(2/3)A - 8 = 2
Add 8 to both sides:
(2/3)A = 10
Multiply both sides by 3:
2A = 30
Divide by 2:
A = 15
Check:
Allowance = $15
Give 1/3 to charity → $5 given, $10 left
Spend $8 → $2 left
✔
✔ Final Answer for #8:
15
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Final Answer:
1. 129
2. 4
3. 11
4. 6
5. 7
6. 55
7. 4, 6, 8
8. 15
Parent Tip: Review the logic above to help your child master the concept of linear system word problems worksheet.
