SOLUTION: Gab’s age on his birthday in 1989 is equal to the sum of the digits of the year 19xy in which he was born. If x and y satisfies the equation x - y - 6 = 0, find the age of Ga
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-> SOLUTION: Gab’s age on his birthday in 1989 is equal to the sum of the digits of the year 19xy in which he was born. If x and y satisfies the equation x - y - 6 = 0, find the age of Ga
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Question 1184410: Gab’s age on his birthday in 1989 is equal to the sum of the digits of the year 19xy in which he was born. If x and y satisfies the equation x - y - 6 = 0, find the age of Gab in 1990. Answer by greenestamps(13200) (Show Source):
Since x and y are both single-digit integers, there are only a few possibilities. Solving the problem by trial and error is probably easier than solving it using formal algebra.
y=0, x=6 ==> he was born in 1960; his age in 1989 was 29; 1+9+6+0 is not equal to 29. Doesn't work.
y=1, x=7 ==> he was born in 1971; his age in 1989 was 18; 1+9+7+1 = 18. It works!
So Gabe was born in 1971.
ANSWER: Gabe's age in 1990 was 1990-1971 = 19
It turns out that a solution using formal algebra is relatively easy....
His age in 1989 is the difference between 89 and "xy", which algebraically is
His age in 1989 is equal to the sum of the digits of the year in which he was born:
Given the restriction that x and y are both single digit positive integers, the only solution to that equation is x=7 and y=1.
Of course you could finish that last step still using formal algebra, knowing that x=y+6:
So again (of course!) we find he was born in 1971, which means his age in 1990 was 19.
