Juan'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 satisfy the equation x-y-6=0, find the age of Juan in 1990.

1
by ichirokhim

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Juan'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 satisfy the equation x-y-6=0, find the age of Juan in 1990.

1
by ichirokhim

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z=10+x+y

x-y-6=0

x-y=6

To find z

-z=-10-x-y

-z=-10-6

-z=-16

z=16

Substitute

z=10+x+y

16=10+x+y

6=x+y

To get x and y

x+y=6

x-y=6

2x=12

x=6

y=0

His age in 1989 is 16 therefore his age in 1980 is 7

*Anyone can correct my solution in case of errors. But in the meantime, here's your answer:)