Three years ago, the ratio of Ali's age to Tika's age was 4:5. If the ratio of their ages three years from now is 5:6, then the difference in their current ages is...
Explanation
Let A be Ali's current age and T be Tika's current age. Given that the ratio of Ali's age to Tika's age three years ago was 4:5.
T−3A−35(A−3)5A−155A−4T=54=4(T−3)=4T−12=3…(1)
Three years from now, the ratio of their ages will be 5:6.
T+3A+36(A+3)6A+186A−5T=65=5(T+3)=5T+15=−3…(2)
From equations (1) and (2), we perform elimination to find the value of A. Multiply equation (1) by 5 and equation (2) by 4.
25A−20T24A−20TA=15=−12=27
Ali's current age is 27 years. Next, we substitute A=27 into equation (1) to find T.
5(27)−4T135−4T4TT=3=3=132=33
Thus, Tika's current age is 33 years. The difference in their ages is:
