Explanation:
Let’s solve each problem one by one, carefully.
Problem 1:
David takes 3 hours to paint a room → his rate = 1/3 of the room per hour.
Sara takes 6 hours → her rate = 1/6 of the room per hour.
Together, their combined rate = 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2 room per hour.
So time to finish 1 room = 1 ÷ (1/2) =
2 hours.
✔ Check: In 2 hours, David paints 2 × (1/3) = 2/3, Sara paints 2 × (1/6) = 1/3 → total = 1 room. Correct.
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Problem 2:
Find three consecutive odd integers: let them be
x, x+2, x+4 (since odd numbers differ by 2).
Given:
2×(first) + (second) + 3×(third) = 152
→ 2x + (x+2) + 3(x+4) = 152
Simplify:
2x + x + 2 + 3x + 12 = 152
→ (2x + x + 3x) + (2 + 12) = 152
→ 6x + 14 = 152
→ 6x = 152 − 14 = 138
→ x = 138 ÷ 6 =
23
So the numbers are: 23, 25, 27.
Check: 2×23 = 46, +25 = 71, +3×27 = 81 → 71 + 81 = 152.
✔
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Problem 3:
Soft drink = $4
8 candy bars = total spent − soft drink = $28 − $4 = $24
So each candy bar = $24 ÷ 8 =
$3
✔ Check: 8 × $3 = $24, + $4 = $28. Correct.
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Problem 4:
Original rectangle: height = 2 m, width = 4 m
Perimeter = 2×(length + width) = 2×(2 + 4) = 12 m
Now width is enlarged to 5 m, perimeter stays 12 m.
Let new length = L
Then: 2×(L + 5) = 12
→ L + 5 = 6
→ L =
1 m
✔ Check: New rectangle: 1 m × 5 m → perimeter = 2×(1+5) = 12 m. Same as before. Correct.
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Problem 5:
One watermelon = $1
With $11, she can buy 11 ÷ 1 =
11 watermelons
✔ Straightforward division.
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Problem 6:
Three consecutive even numbers: let them be
x, x+2, x+4
Sum = x + (x+2) + (x+4) = 3x + 6 = 156
→ 3x = 156 − 6 = 150
→ x = 150 ÷ 3 =
50
So smallest number =
50
✔ Check: 50 + 52 + 54 = 156. Correct.
Final Answer:
1) 2 hours
2) 23, 25, 27
3) $3
4) 1 m
5) 11
6) 50
Parent Tip: Review the logic above to help your child master the concept of linear equations worksheet 8th grade.
