The age of Mwenda is 3/5 of that of his sister.If 20 years ago the age of Mwenda was 2/5 of that of his sister then. Find the present age of Mwend.
#Please guys help me this question#
Age of Mwenda = x
Age of Mwenda's sister = y
i) x = (3/5)*y
ii) (x - 20) = (2/5)*(y - 20)
Now, put 'x = (3/5)y' into the second equation.
=> ((3/5)*y - 20) = (2/5)*(y - 20)
Solve for y, then for x.
Do the word "then" in sentence has no effect because then it means now i think on equation 2 how will it be or is like the way which you solved
To solve this problem, let's assume the present age of Mwenda is represented by "M" and the present age of his sister is represented by "S".
According to the problem, the age of Mwenda is 3/5 of his sister's age. This can be represented as:
M = (3/5) * S -- Equation 1
The problem also states that 20 years ago, the age of Mwenda was 2/5 of his sister's age. We can represent this as:
(M - 20) = (2/5) * (S - 20) -- Equation 2
Now we can solve these two equations simultaneously to find the values of M and S.
To do this, we can rearrange Equation 1 to solve for S:
S = (5/3) * M
Substituting this value of S in Equation 2, we get:
(M - 20) = (2/5) * ((5/3) * M - 20)
Expanding and simplifying the equation, we get:
5M - 100 = 2(5M/3 - 20)
Multiply through by 3 to eliminate the fractions:
15M - 300 = 2(5M - 60)
Expanding again, we get:
15M - 300 = 10M - 120
Simplifying further:
5M = 180
Divide both sides by 5:
M = 36
Therefore, the present age of Mwenda (M) is 36 years.
To find the present age of Mwenda's sister (S), we substitute this value back into Equation 1:
S =(5/3) * M
S =(5/3) * 36
S = 60
Therefore, the present age of Mwenda's sister (S) is 60 years.
So, Mwenda's present age is 36 years and his sister's present age is 60 years.