Five years ago Kate was five times as
old as her son.
Five years hence her age will be
eight lessthan three times the
corresponding age of her son. Find their present ages.
Let Kate = k, let her son = s
k - 5 = 5(s - 5)
(You have to take 5 years from both their ages)
k = 5s - 20 (1)
k + 5 = 3(s + 5) - 8
k = 3s + 2 (2)
sub (2) into (1)
5s - 20 = 3s + 2
2s = 22
s = 11
sub into (1)
k = 5 x 11 - 20
k = 35
Let's assume Kate's current age as "K" and her son's current age as "S".
According to the given information:
1) Five years ago, Kate was five times as old as her son.
So, (K - 5) = 5(S - 5)
2) Five years hence (in the future), her age will be eight less than three times the corresponding age of her son.
So, (K + 5) = 3(S + 5) - 8
Now we have a system of two equations. Let's solve it step-by-step.
First, expand the equations:
1) K - 5 = 5S - 25
2) K + 5 = 3S + 15 - 8
Simplifying the equations:
1) K - 5 = 5S - 25
K - 5S = -20 ......(Equation 1)
2) K + 5 = 3S + 7
K - 3S = 2 ......(Equation 2)
Now we can solve this system of equations using any method. Let's use the method of substitution:
From Equation 1, we can express K in terms of S:
K = 5S - 20
Substituting the value of K in Equation 2:
5S - 20 - 3S = 2
2S = 22
S = 11
Now substitute the value of S back into Equation 1:
K - 5(11) = -20
K - 55 = -20
K = -20 + 55
K = 35
So, Kate's present age (K) is 35, and her son's present age (S) is 11.
To solve this problem, let's assign variables to represent the present ages of Kate and her son.
Let's say the present age of Kate is represented by "K" and the present age of her son is represented by "S".
According to the first statement, five years ago, Kate was five times as old as her son. This can be written as:
K - 5 = 5(S - 5) (Equation 1)
According to the second statement, five years from now, Kate's age will be eight less than three times the corresponding age of her son. This can be written as:
K + 5 = 3(S + 5) - 8 (Equation 2)
Now we have two equations (Equation 1 and Equation 2) with two unknowns (K and S). We can solve these equations simultaneously to find the values of K and S.
Let's simplify Equation 1:
K - 5 = 5S - 25 (Distributing the 5 into S and -5)
K = 5S - 20 (Adding 5 to both sides)
Now let's substitute this value of K into Equation 2:
5S - 20 + 5 = 3(S + 5) - 8 (Substituting K = 5S - 20)
5S - 15 = 3S + 15 - 8 (Simplifying)
5S - 15 = 3S + 7 (Combining like terms)
2S = 22 (Subtracting 3S from both sides and adding 15 to both sides)
S = 11 (Dividing both sides by 2)
Now that we have the value of S, we can substitute it back into Equation 1 to find the value of K:
K = 5(11) - 20 = 55 - 20 = 35
Therefore, the present age of Kate (K) is 35 and the present age of her son (S) is 11.