kate is twice as old as her sister mars. the sum of their ages is 24. find their ages. Let k be Kate's age Let m be Mars's age We're given two equations: k = 2m. (Because twice means multiply by 2) k + m = 24 Substitute equation (1) for k into equation (2): 2m + m = 24 T o solve for m, we type this equation into our math engine: m = 8 We want to solve for k using m= 8. Substitute this into equation 1 k = 2(8) k = 16 Check our work for equation 1 16 = 2 * 8 16 = 16 Check our work for equation 2 16 + 8 ? 24 24 = 24