Question 1062753: When santy and lorna were married, his age was 3/2 of her age. If on their golden wedding anniversary, Santy's age will be 8/7 of lorna's age, how old will each of them be on their golden anniversary. Show algebraic solution
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! when they got married, he was 30 and she was 20.
the ratio of their ages was 3/2.
50 years later, he was 80 and she was 70.
the ratio of their ages was 8/7.
to solve this algebraically, you can do the following.
let a = his age when they got married.
let b = her age when they got married.
you get a/b = 3/2.
solve for a to get a = 3/2 * b.
50 years later his age is a + 50.
50 years later her age is b + 50.
you get (a + 50) / (b + 50) = 8/7
solve for (a + 50) to get (a + 50) = 8/7 * (b + 50).
solve for a to get a = 8/7 * (b + 50) - 50
this means that 3/2 * b = 8/7 * (b + 50) - 50 because they are both equal to a.
multiply both sides of this equation by 2/3 and you get:
b = 2/3 * 8/7 * (b + 50) - 2/3 * 50
since 2/3 * 8/7 is equal to 16/21 and since 2/3 is equal to 14/21, this equation becomes:
b = 16/21 * (b + 50) - 14/21 * 50
simplify this to get:
b = 16/21 * b + 16/21 * 50 - 14/21 * 50
combine like terms to get:
b = 16/21 * b + 2/21 * 50
subtract 16/21 * b from both sides of this equation to get:
b - 16/21 * b = 2/21 * 50
since b = 21/21 * b, this becomes:
21/21 * b - 16/21 * b = 2/21 * 50
combine like terms to get 5/21 * b = 2/21 * 50
multiply both sides of this equation by 21 to get 5 * b = 2 * 50
simplify to get 5 * b = 100
divide both sides of this equation by 5 to get b = 20
since a = 3/2 * b, you get a = 30
50 years later you get a + 50 = 80 and b + 50 = 70
the ratio of their ages is 30/20 = 3/2 when they got married.
the ratio of their ages is 80/70 = 8/7 on their golden wedding anniversary.
Answer by ikleyn(52776)  (Show Source):
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