jack's age was 2/5 of the age je will be 20 years from now 7 years ago. How old in Jack?

Answer 1

This sounds confusing, but once you figure out the phrasing, it's not so hard. Let's rearrange the question to make some more sense: Jack's age 7 years ago is the same as 2/5th of his age in 20 years. Let's have J represent Jack. So Jack's age 7 years ago, is J-7. His age then was equal to 2/5(J+20). This is because his age is a portion of what it is in 20 years, which is itself J+20. Since these are equal, let's make them an equation: J-7 = 2/5(J+20). Now let's do the multiplication: J-7 = 2/5J + 8. Add 7 to both sides. J=2/5J + 15. Now let's multiple everything by 5 to get rid of our fraction. 5J = 2J + 75. Now subtract 2J from either side. 3J = 75. Now divide by 3. J=25. Remember, this is his age currently. Let's double-check our work with the original problem. Seven years ago, Jack would have been 25-7 = 18. This should equal 2/5 of his age in 20 years (2/5 (J+20)). 2/5th (25+20) = 2/5(45) = 18. Which is how old he was 7 years ago! Hope that helped. :)