1. Stating the problem: We are given two equations based on Kieran's and Louise's numbers. Let Kieran's number be $k$ and Louise's number be $l$. 2. From the problem, translate into equations: "4 less than Kieran's number is equal to 2 lots of Louise's number" means: $$k - 4 = 2l$$ "3 lots of Kieran's number added to Louise's number is 68" means: $$3k + l = 68$$ 3. Solve the system of equations: From equation 1: $$k - 4 = 2l \implies k = 2l + 4$$ Substitute $k$ into equation 2: $$3(2l + 4) + l = 68$$ Simplify: $$6l + 12 + l = 68$$ $$7l + 12 = 68$$ Subtract 12: $$7l = 56$$ Divide by 7: $$l = 8$$ 4. Find $k$ using $l = 8$: $$k = 2(8) + 4 = 16 + 4 = 20$$ 5. Final answer: Kieran's number is $20$ and Louise's number is $8$.