This year Grandma's age and Mother's age are the same but with the digits reversed. One year ago, Grandma was twice as old as Mother. How old are Grandma and Mother today?
2 answers
73 and 37
grandma's age --- 10x + y
mother's age ---- 10y + x
one year ago:
grandma : 10x+y - 1
mothers: 10y+x - 1
10x+y - 1 = 2(10y+x-1)
10x + y - 1 = 20y + 2x - 2
8x - 19y = -1
8x = 19y-1
x = (19y-1)/8
try different y's so that the numerator is a multiple of 8
e.g. when y = 3, x = 7 , the only one that works
so grandma is 73, the mother is 37
check: one year ago, grandma was 72, and mother was 36, and 72 is twice 36
mother's age ---- 10y + x
one year ago:
grandma : 10x+y - 1
mothers: 10y+x - 1
10x+y - 1 = 2(10y+x-1)
10x + y - 1 = 20y + 2x - 2
8x - 19y = -1
8x = 19y-1
x = (19y-1)/8
try different y's so that the numerator is a multiple of 8
e.g. when y = 3, x = 7 , the only one that works
so grandma is 73, the mother is 37
check: one year ago, grandma was 72, and mother was 36, and 72 is twice 36