Currently, the ratio of Jaeden’s age to Kiernan’s age is 5:3, and the sum of their ages is 32. In 10 years, the ratio of their ages will be _________.

Let 5x = Jaeden’s current age, and 3x = Kiernan’s current age. Then 5x + 3x = 32, so 8x = 32 and x = 4. Thus, Jaeden’s current age is 5x = 5(4) = 20, and Kiernan’s current age is 3x = 3(4) = 12. In 10 years, Jaeden and Kiernan will be 30 and 22, respectively, and the ratio of their ages will be \( \frac{\mathrm{30} }{\mathrm{22}}= \frac{\mathrm{15} }{\mathrm{11}}\) , which is 15:11.