1. Three consecutive natural numbers add up to 24 . Find the numbers. 2. A mother is three times as old as her daughter. In 12 years' time she will be twice as old as her daughter will be then. How old is the mother now? 3. The perimeter of a rectangular flower bed is 26 m . If the length exceeds the breadth by 3 m , find its dimenin

To solve for the three consecutive natural numbers that add up to 24, we can represent them as \( x, x+1, \) and \( x+2 \). Setting up the equation: \( x + (x + 1) + (x + 2) = 24 \). Simplifying this results in \( 3x + 3 = 24 \), which leads to \( 3x = 21 \), so \( x = 7 \). Therefore, the three consecutive numbers are 7, 8, and 9! Now, regarding the age problem involving the mother and daughter, let’s denote the daughter’s current age as \( d \). Then, the mother’s age can be expressed as \( 3d \). In 12 years, the mother will be \( 3d + 12 \) and the daughter will be \( d + 12 \). Setting up the equation \( 3d + 12 = 2(d + 12) \) simplifies to \( 3d + 12 = 2d + 24 \), leading to \( d = 12 \). The mother is currently \( 3d = 36 \) years old! For the flower bed dimensions, start by letting the breadth be \( b \). Then, the length becomes \( b + 3 \). The perimeter is given by the formula \( P = 2(length + breadth) = 26 \), leading to \( 2[(b + 3) + b] = 26 \). Simplifying gives us \( 2(2b + 3) = 26 \) or \( 2b + 3 = 13 \). Solving for \( b \) shows \( 2b = 10 \) so \( b = 5 \). Consequently, the length is \( 5 + 3 = 8 \). Therefore, the dimensions are 8 m for length and 5 m for breadth!