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put this solution on YOUR website!Let's first consider the relationship of their ages NOW. If Aaron is 24 years younger than his father, his age A = F - 24. AKA, his father is 24 years older, so to get from his father's age to his age, we must subtract 24 years from the father's age. So far, we chose the father's age to be F, and Aaron's age to be F - 24. We need to express both ages in one variable so that we'll be able to solve an equation in just one variable.
Now, in 10 years, they'll still be 24 years apart, but the ratio between their ages CHANGES. In 10 years, the father's age will obviously by F + 10. Aaron's age will be (F - 24) + 10, simplified to F - 14. Aaron's father will be 3x older than Aaron. This means that since Aaron's father will be 3x older, we need to multiply Aaron's age by 3 to equal his father's:
<---- This is the "10 years into the future" configuration. The father will be 3x older than Aaron. (WARNING: Many might think that we should multiply the father's age by 3 because he's older. It's actually the opposite. He's already older. Why blow up his age more? It's Aaron's age that needs to be blown up 3 times to equal his father's age!)
<---- Distributed
<----- Subtracted F from both sides. Notice that it's better to have the variable on the right side of the equation since it will be positive then. We got subconsciously used to having the variable to the left of the equals sign.
<---- Added 42 to both sides.
<----- Aaron's father is currently 26 years old. If Aaron is 24 years younger, Aaron would be 2.
Now, in 10 years, Aaron's father would be 36, and aaron would be 12. We're right on because 36 is triple 12, just like the problem said about how much the father's age is compared to Aaron's after the 10 years.
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