1. Let the time taken by David and Sara together be \( t \) hours.
David's rate: \( \frac{1}{3} \) room per hour
Sara's rate: \( \frac{1}{6} \) room per hour
Combined rate: \( \frac{1}{3} + \frac{1}{6} = \frac{1}{2} \) room per hour
So, \( \frac{1}{2} \times t = 1 \) → \( t = 2 \) hours.
Answer: 2 hours.
2. Let the three consecutive odd integers be \( x \), \( x+2 \), \( x+4 \).
Given: \( 2x + (x+2) + 3(x+4) = 152 \)
Simplify: \( 2x + x + 2 + 3x + 12 = 152 \) → \( 6x + 14 = 152 \)
\( 6x = 138 \) → \( x = 23 \)
So the integers are 23, 25, 27.
Answer: 23, 25, 27.
3. Let the cost of each candy bar be \( x \) dollars.
Total cost: \( 4 + 8x = 28 \)
\( 8x = 24 \) → \( x = 3 \)
Answer: $3.
4. Original rectangle: height = 2 m, width = 4 m
Perimeter: \( 2(2 + 4) = 12 \) m
New width = 5 m, let new length = \( l \)
New perimeter: \( 2(l + 5) = 12 \) → \( l + 5 = 6 \) → \( l = 1 \) m
Answer: 1 m.
5. Watermelon costs $1 each.
Number of watermelons for $11: \( \frac{11}{1} = 11 \)
Answer: 11.
6. Let the three consecutive even numbers be \( x \), \( x+2 \), \( x+4 \).
Sum: \( x + (x+2) + (x+4) = 156 \) → \( 3x + 6 = 156 \)
\( 3x = 150 \) → \( x = 50 \)
Answer: 50.
Parent Tip: Review the logic above to help your child master the concept of solving algebra word problems worksheet.
