Grandmother is 3 years younger than grandfather. Nine years ago, the sum of their ages was 105. How old are they?
Now:
grandpa --- x
grandma --- x-3
nine years ago:
grandpa ---- x-9
grandma ---- x-3 - 9 = x - 12
translate "Nine years ago, the sum of their ages was 105" into math
x-9 + x-12 = 105
carry on ....
X-9+x-12=105
X+x=105+9+12
2x=126
X=63
Grandmother x-3
63-3=60
Grandfather x
63
Let's break down the information given:
Let's assume the grandmother's age is G and the grandfather's age is F.
From the first statement, "Grandmother is 3 years younger than grandfather," we can write an equation:
G = F - 3 ...(equation 1)
From the second statement, "Nine years ago, the sum of their ages was 105":
- Nine years ago, the grandmother's age would have been G - 9.
- Nine years ago, the grandfather's age would have been F - 9.
The sum of their ages, nine years ago, would be 105:
(G - 9) + (F - 9) = 105
Now, let's substitute G from equation 1 into the equation above:
(F - 3 - 9) + (F - 9) = 105
F - 12 + F - 9 = 105
2F - 21 = 105
2F = 105 + 21
2F = 126
F = 126 / 2
F = 63
Now, we can substitute the value of F back into equation 1 to find G:
G = 63 - 3
G = 60
Therefore, the grandfather is 63 years old and the grandmother is 60 years old.