The total initial cost of labour, materials, and contractor's charges is $64,000.00. The ratio of labour, materials, and contractor's charges is 12:15:5. The cost of labour increased by x%. The cost o

Step 1: Calculate the initial costs of labour, materials, and contractor's charges. The total initial cost is 64,000.00. The ratio of labour, materials, and contractor's charges is 12 : 15 : 5. The total number of ratio parts is 12 + 15 + 5 = 32. Initial cost of labour (L_0): L_0 = (12)/(32) × 64000 = 12 × 2000 = 24000 Initial cost of materials (M_0): M_0 = (15)/(32) × 64000 = 15 × 2000 = 30000 Initial contractor's charges (C_0): C_0 = (5)/(32) × 64000 = 5 × 2000 = 10000 Step 2: Express the new costs after the increases. The cost of labour increased by x \%. The new cost of labour (L_1) is: L_1 = L_0 (1 + (x)/(100)) = 24000 (1 + (x)/(100)) The cost of materials increased by 2x \%. The new cost of materials (M_1) is: M_1 = M_0 (1 + (2x)/(100)) = 30000 (1 + (2x)/(100)) The contractor's charges (C_1) remained the same: C_1 = C_0 = 10000 Step 3: Use the given condition to find the value of x. After the increase, the cost of labour was two-thirds the cost of materials: L_1 = (2)/(3) M_1 Substitute the expressions for L_1 and M_1: 24000 (1 + (x)/(100)) = (2)/(3) × 30000 (1 + (2x)/(100)) 24000 (1 + (x)/(100)) = 20000 (1 + (2x)/(100)) Divide both sides by 1000: 24 (1 + (x)/(100)) = 20 (1 + (2x)/(100)) Divide both sides by 4: 6 (1 + (x)/(100)) = 5 (1 + (2x)/(100)) Expand the equation: 6 + (6x)/(100) = 5 + (10x)/(100) Multiply by 100 to clear denominators: 600 + 6x = 500 + 10x Rearrange terms to solve for x: 600 - 500 = 10x - 6x 100 = 4x x = (100)/(4) x = 25 a) The value of x: 25 Step 4: Calculate the new cost of building the restaurant. Substitute x=25 into the expressions for L_1 and M_1: L_1 = 24000 (1 + (25)/(100)) = 24000 (1 + 0.25) = 24000 × 1.25 = 30000 M_1 = 30000 (1 + (2 × 25)/(100)) = 30000 (1 + (50)/(100)) = 30000 (1 + 0.5) = 30000 × 1.5 = 45000 The contractor's charges remain C_1 = 10000. The new total cost of building the restaurant is the sum of the new costs: New total cost = L_1 + M_1 + C_1 = 30000 + 45000 + 10000 = 85000 b) The new cost of building the restaurant: \85,000.00 Send me the next one 📸