Let’s solve each problem one by one, step by step.
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Problem 1:
David takes 3 hours to paint a room → So in 1 hour, he paints
1/3 of the room.
Sara takes 6 hours → So in 1 hour, she paints
1/6 of the room.
Together, in 1 hour, they paint:
1/3 + 1/6 = 2/6 + 1/6 =
3/6 = 1/2 of the room.
So if they paint half the room in 1 hour, it will take them
2 hours to paint the whole room.
✔ Check: In 2 hours, David paints 2 × (1/3) = 2/3. Sara paints 2 × (1/6) = 1/3. Total = 2/3 + 1/3 = 1 → Whole room. Correct.
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Problem 2:
We need three consecutive odd integers. Let’s call them:
First: x
Second: x + 2
Third: x + 4
“Sum of twice the first, the second, and three times the third is 152”
That means:
2×(first) + (second) + 3×(third) = 152
→ 2x + (x + 2) + 3(x + 4) = 152
Now simplify:
2x + x + 2 + 3x + 12 = 152
Combine like terms:
(2x + x + 3x) + (2 + 12) = 152
6x + 14 = 152
Subtract 14 from both sides:
6x = 138
Divide by 6:
x = 23
So the numbers are:
23, 25, 27
✔ Check: Twice first = 46, second = 25, three times third = 81 → 46 + 25 + 81 = 152. Correct.
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Problem 3:
Nancy bought:
- 1 soft drink for $4
- 8 candy bars (unknown price each)
Total spent: $28
Let cost of one candy bar = c
Equation:
4 + 8c = 28
Subtract 4 from both sides:
8c = 24
Divide by 8:
c = 3
Each candy bar costs
$3
✔ Check: 8 × 3 = 24, plus 4 = 28. Correct.
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Problem 4:
Original rectangle:
Height = 2 m, Width = 4 m
Perimeter = 2×(height + width) = 2×(2 + 4) = 2×6 =
12 meters
New width = 5 m
Perimeter stays same = 12 m
Let new height = h
Perimeter formula: 2×(h + 5) = 12
Divide both sides by 2:
h + 5 = 6
Subtract 5:
h = 1
New length (height) is
1 meter
✔ Check: 2×(1 + 5) = 2×6 = 12. Same perimeter. Correct.
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Problem 5:
Mary buys 1 watermelon for $1 → So each costs $1.
How many can she buy for $11?
Just divide: 11 ÷ 1 =
11
She can buy
11 watermelons
✔ Simple check: 11 × $1 = $11. Correct.
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Problem 6:
Three consecutive even numbers. Let’s say:
Smallest: x
Next: x + 2
Next: x + 4
Sum = 156
So: x + (x + 2) + (x + 4) = 156
Combine: 3x + 6 = 156
Subtract 6: 3x = 150
Divide by 3: x = 50
Smallest number is
50
✔ Check: 50 + 52 + 54 = 156. Correct.
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Final Answer:
1. 2 hours
2. 23, 25, 27
3. $3
4. 1 meter
5. 11
6. 50
Parent Tip: Review the logic above to help your child master the concept of using equations to solve word problems worksheet.
