A mother is x years old, her son is y years old and the sum of theirs ages together is 58 years. Five years ago, the mother was five times as old as the son. Write two equations in x and y and solve them to find the age of their mother and age of the son.

I have found out the answer, but the problem is that I do not know the METHOD of finding the answer.
Please reply asap if you are able. Thank You.

Answers:

Mother = 45
Son = 13

the method is just to write the words as math:

mother is x years old, her son is y years old and the sum of theirs ages together is 58

x+y = 58

Five years ago, the mother was five times as old as the son

(x-5) = 5(y-5)

Now it's easy!

x+y=58
x-5y = -20

subtract and you get

6y = 78
y = 13
so, x=58-y = 45

5 years ago they were 40 and 8; 40=5*8

How do you get x-5y = -20

Sure, I can help you with that. Let's start with the equations:

1. The sum of their ages together is 58 years: x + y = 58
2. Five years ago, the mother was five times as old as the son: (x - 5) = 5(y - 5)

Now, let's solve these equations:

First, let's simplify equation 2:
x - 5 = 5y - 25
x = 5y - 20

Now, substitute this value of x in equation 1:
5y - 20 + y = 58
6y - 20 = 58
6y = 78
y = 13

Substitute the value of y in equation 1 to find the value of x:
x + 13 = 58
x = 58 - 13
x = 45

So, the age of the mother is 45 years and the age of the son is 13 years.

To solve this problem, we can set up two equations based on the given information.

1) The sum of their ages together is 58: x + y = 58

2) Five years ago, the mother was five times as old as the son: x - 5 = 5(y - 5)

Now, let's solve these equations step by step.

Step 1: Rearrange equation 2 for x in terms of y:
x - 5 = 5y - 25
x = 5y - 20

Step 2: Substitute the value of x from equation 2 into equation 1:
5y - 20 + y = 58
6y - 20 = 58

Step 3: Add 20 to both sides of the equation:
6y = 78

Step 4: Divide both sides of the equation by 6:
y = 13

Step 5: Substitute the value of y into equation 1 to find x:
x + 13 = 58
x = 58 - 13
x = 45

Therefore, the mother is 45 years old and the son is 13 years old.

To solve this problem, we can set up a system of equations based on the given information.

Let's assign the variables x and y to represent the age of the mother and the son, respectively.

Based on the given information, we can come up with two equations:

1) "A mother is x years old, her son is y years old and the sum of their ages together is 58 years" can be written as: x + y = 58.

2) "Five years ago, the mother was five times as old as the son" can be written as: (x - 5) = 5 * (y - 5).

Now, we have a system of two equations:

x + y = 58, ----(1)
x - 5 = 5(y - 5). ----(2)

To solve the system of equations, we can use the substitution method or the elimination method. Let's use the substitution method in this case.

From equation (1), we can express x in terms of y by subtracting y from both sides:
x = 58 - y.

Substituting the value of x in equation (2), we get:
58 - y - 5 = 5(y - 5).

Simplifying the equation:
53 - y = 5y - 25.

Adding y to both sides and subtracting 53 from both sides:
5y + y = 53 + 25,
6y = 78.

Dividing both sides by 6:
y = 78 / 6,
y = 13.

Now, we can substitute the value of y into equation (1) to find x:
x + 13 = 58,
x = 58 - 13,
x = 45.

Therefore, the age of the mother is 45 years and the age of the son is 13 years.