5 years ago, the ratio of Raymond's age to Rachel's age was 3 : 7.The ratio of Raymond's age to Rachel's age has become 2 : 3 now.How old is Rachel now?
Question
5 years ago, the ratio of Raymond's age to Rachel's age was 3 : 7.The ratio of Raymond's age to Rachel's age has become 2 : 3 now.How old is Rachel now?
Solution
Let's denote Raymond's age 5 years ago as 3x and Rachel's age 5 years ago as 7x.
According to the problem, the ratio of their ages now is 2:3. But since 5 years have passed, their current ages are 3x+5 and 7x+5 respectively.
So, we can set up the equation (3x+5)/(7x+5) = 2/3.
Cross-multiplying gives us 9x + 15 = 14x + 10.
Solving this equation for x gives us x = 1.
Substituting x = 1 back into the equation for Rachel's age 5 years ago gives us Rachel's age 5 years ago as 7*1 = 7.
Adding 5 to this gives us Rachel's current age as 7 + 5 = 12.
So, Rachel is 12 years old now.
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