Question

Mr me hats is three times as old as his daughter and the sum of their ages to is 48 from an equation for this situation and then find their ages

Answer 1

Question :

A man is three times as old as his daughter and the sum of their ages to is 48 from an equation for this situation and then find their ages.

Step by step solution :

Let x be the age of the son,

and y be the age of the man.

ATQ, the equation -

y = 3x

x + y = 48

There are now two easy ways to solve this with equations, substitution, and elimination.

SUBSTITUTION :

Since we know that y = 3x, we can substitute the y in the second equation with 3x, giving us x + y = 48.

So,

x + y = 48

x + 3x = 48

4x = 48

x = 12

The Kid is 12 years old.

The Man is 3 × 12 = 36 years old.

ELIMINATION :

Another way we can solve this is by using elimination. In this problem, it might be easier if we rearrange things a bit :

If we subtract each side from 3x in the first equation, we now have:

y - 3x = 0

and since we have the commutative property in addition, just swap the positions of the x and y in the second equation:

y + x = 48

Those steps were unnecessary, but visually, can help make the solution make more sense.

Since we know have :

y - 3x = 0

y + x = 48

We can just subtract them from each other to get rid of the y. Remember to subtract the terms correctly, or else, you might get the wrong answer.

y - 3x - ( y + x ) = 0 - 48

-4x = -48

We now have the equation:

-4x = -48

Divide both sides by -4, giving us:

x = 12

So, the son is 12 years old.

Sometimes it is good to try both ways to check your work.