Sandra is eight yrs younger than her brother mike. six yrs ago mike was three times old of Sandra. how old is mike? how old is Sandra?
34+7
s = m - 8
m - 6 = 3(s - 6) = 3 s - 18
m - 8 = 3 s - 20
susbstituting
... s = 3 s - 20
... 20 = 2 s
mike's age ---- x years
Sandra's age --- x-8 years
Six years ago:
Mike was x - 6
Sandra was x-8-6 = x-14
x-6 = 3(x-14)
x-6 = 3x - 42
36 = 2x
x = 18
Mike is now 18 and Sandra is now 10 years old
check:
6 years ago Mike was 12 and Sandra was 4
which is 3 times as old
My answer is correct
To solve this problem, we need to set up equations based on the given information.
Let's assume Mike's age is M and Sandra's age is S.
According to the problem, Sandra is eight years younger than Mike, so we can write the equation:
S = M - 8 ---(1)
Six years ago, Mike was three times older than Sandra. To determine their ages back then, we subtract 6 from both M and S:
(M - 6) = 3(S - 6) ---(2)
Now we have two equations (equations 1 and 2) with two unknowns (M and S). We can solve these equations simultaneously to find the values of M and S.
First, we can simplify equation 2 by expanding the brackets:
M - 6 = 3S - 18
M = 3S - 12 ---(3)
Now we can substitute equation 3 into equation 1 to eliminate M and solve for S:
S = (3S - 12) - 8
S = 3S - 20
-2S = -20
S = 10
So, Sandra is 10 years old.
To find Mike's age, we substitute the value of S into equation 1:
M = S + 8
M = 10 + 8
M = 18
Therefore, Mike is 18 years old.