Please explain step by step by k=2l/3 not k=3l/2?

A firm has a production function Q = F (K, L) with constant returns to scale. Input prices are r = 2 and w = 1. The output-expansion path for this production function at these input prices is a straight line through the origin. When the firm produces 5 units of output, it uses 2 units of K and 3 units of L. How much K and L will it use when its long-run total cost is equal to 70? ANSWER For this production function, as long as the input price ratio ( r / w) remains 2:1, the optimal input bundle will always have 2 units of capital for every 3 units of labour, i.e., K = 2L / 3. For a total cost of 70, we thus have rK + wL = 2(2L / 3) + L = 70, which solves fort. = 30 and K = 20. (See diagram.) K 35 Output Exansion Path (slope = 2/3) 20