A mother is three times as old as her son. Eight years ago, she was 4 more than five times the age of her son. How old is the mother now?
son's age ---- x
mother ------ 3x
eight yrs ago:
son ---- x-8
mom --- 3x-8
3x-8 = 5(x-8) + 4
3x-8 = 5x-40+4
-2x = -28
x = 14
mother now is 3x = 42
check:
now:
son--- 14
mom ---42
8 yrs ago:
son =6
mom = 34
is 34 four more than 5x6 ?? YES
To solve this problem, we can set up a system of equations. Let's denote the age of the son as S, and the age of the mother as M.
From the problem statement, we have two pieces of information:
1) "A mother is three times as old as her son" translates to M = 3S.
2) "Eight years ago, she was 4 more than five times the age of her son" translates to M - 8 = 5(S - 8) + 4.
Now, we can substitute the value of M from the first equation into the second equation to solve for S:
3S - 8 = 5(S - 8) + 4
3S - 8 = 5S - 40 + 4
3S - 8 = 5S - 36
2S = 28
S = 14
Now that we know the age of the son is 14, we can substitute it back into the first equation to find the age of the mother:
M = 3S
M = 3(14)
M = 42
Therefore, the mother is 42 years old.