Three clients need a rough estimate of what their houses will cost them with similar fittings. To develop a property, the \( R / \mathrm{m}^{2} \) (rand per square meter) usually shows that the larger the house the cheaper the cost per square meter that a customer pays. The floor area of client A's house is three times larger than client B's and the floor area of client \( C \) is half the size of client \( A \). The total floor area of all the houses is \( 682 \mathrm{~m}^{2} \). a) Calculate the floor area of each house.

Let's denote the floor area of client B's house as \( x \). According to the problem, we know the following relationships: - Client A's house is three times larger than client B's, so the floor area of client A's house is \( 3x \). - Client C's house is half the size of client A's, so the floor area of client C's house is \( \frac{3x}{2} \). Now, we can express the total floor area of all the houses in terms of \( x \): \[ x + 3x + \frac{3x}{2} = 682 \] Combining the terms on the left: \[ 4x + \frac{3x}{2} = 682 \] To eliminate the fraction, we can multiply the entire equation by 2: \[ 8x + 3x = 1364 \] This simplifies to: \[ 11x = 1364 \] Dividing both sides by 11 gives us: \[ x = \frac{1364}{11} = 124 \] Now we can find the floor areas for each client: - Client B's house: \( x = 124 \, \mathrm{m}^{2} \) - Client A's house: \( 3x = 3 \times 124 = 372 \, \mathrm{m}^{2} \) - Client C's house: \( \frac{3x}{2} = \frac{3 \times 124}{2} = 186 \, \mathrm{m}^{2} \) To summarize: - Client A's house: \( 372 \, \mathrm{m}^{2} \) - Client B's house: \( 124 \, \mathrm{m}^{2} \) - Client C's house: \( 186 \, \mathrm{m}^{2} \)