Question #d3d11

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Question #d3d11

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Answer 1 · 2017-08-08T17:44:35

The father is 24 years old, and the son is 6 years old.

Explanation:

Let x represent the son's age.
Let y represent the man's age.

Make two equations:

(1) The man's age is equal to four times his son's age:

$y = 4 x$ $y = 4x$

(2) In three years the man's age will be $y + 3$ $y + 3$ .
In three years the son's age will be $x + 3$ $x + 3$ .
In three years the man's age will be equal to three times his son's age.

$y + 3 = 3 (x + 3)$ $y + 3 = 3 (x+3)$

Expand the second equation:

$y + 3 = 3 (x + 3)$ $y + 3 = 3 (x+3)$

$y + 3 = 3 x + 9$ $y + 3 = 3x+9$

Equate the two equations:

Since $y = 4 x$ $y = 4x$ , you can replace the $y$ $y$ in the second equation with $4 x$ $4x$

$y + 3 = 3 x + 9$ $y + 3 = 3x+9$

$4 x + 3 = 3 x + 9$ $4x + 3 = 3x+9$

Simplify the equation:

$4 x + 3 = 3 x + 9$ $4x + 3 = 3x+9$

$4 x - 3 x + 3 = 9$ $4x-3x+3= 9$

$4 x - 3 x = 9 - 3$ $4x-3x=9-3$

$x = 6$ $x=6$

Substitute this value into the first equation:

$y = 4 x$ $y = 4x$

$y = 4 (6)$ $y = 4(6)$

$y = 24$ $y = 24$

Therefore the son's age $(x)$ $(x)$ is 6 years and the man's age $(y)$ $(y)$ is 24 years.

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Question #d3d11

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