Depth · one concept from first principles · step 2 of 4
A man is now years older than his wife. years ago, he had been married for exactly half of the life he had lived so far. years from now, his wife will have been married for of her life. How old was the man on the couple's th wedding anniversary?
Let the man be x years old now; then his wife is x - 4.
One unknown is enough, because the two ages differ by a fixed 4.
7.EE.B.4Convert To Algebra6 years ago he was x - 6 and had been married half of that. Six more years have passed since, so today the marriage is 6 years longer.
On a timeline, the marriage length grows by exactly the years that pass.
7.EE.B.4Draw A DiagramIn 13 years she will be (x - 4) + 13 = x + 9 and married for 2/3 of that. Today is 13 years earlier, so subtract 13.
The same timeline, read from the other end.
7.EE.B.4Draw A DiagramBoth expressions count the same marriage. Multiply both sides by 6 to clear the fractions.
Clearing denominators turns it into a one-step linear equation.
7.EE.A.2Convert To AlgebraThe husband's clue and the wife's clue give the same number of years married today: .
Both expressions count the same marriage on the same day, so being equal to that one number makes them equal to each other.
From the husband's side: years ago he was and married for half of it, and more years of marriage have passed since.
Half his life then is his age split into two equal shares, one of them taken: .
Age and marriage length both grow by one year each year, so years later both are larger.
From the wife's side: in years she will be and married for of that, so today the marriage is years shorter.
Both of them age one year per year, so the wife stays years younger: .
The marriage grows by one year each year, so going back years takes off its length.
Today they have been married (1/2)(60-6)+6 = 27+6 = 33 years. The 30th anniversary was 33 - 30 = 3 years ago.
The question asks for a different moment than the one we solved for, so one more subproblem is needed.
7.EE.B.3Identify SubproblemsWhen two clues describe the same quantity, write it both ways and set them equal.
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