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Question: Two years ago, my age was four times the age of my son, eight years ago my age was ten times the age of my son find the age of my son now This question has already been explained by my friend, but I don't get how she knew she had to get the dad's age in terms of sons age, + 6 to it, and then solve it. Someone please explain

Respuesta :

MrRoyal

Answer:

My age is 38 years old

My son is 11 years old

Step-by-step explanation:

Represent my current age with x and my son's current age with y

Two years ago;

[tex]x - 2 = 4 * (y - 2)[/tex]

Eight years ago:

[tex]x - 8 = 10 * (y - 8)[/tex]

Simplify both expressions

[tex]x - 2 = 4 * (y - 2)[/tex]

[tex]x - 2 = 4y - 8[/tex]

Add 2 to both sides

[tex]x - 2 +2= 4y - 8 + 2[/tex]

[tex]x = 4y - 6[/tex]

Substitute 4y - 6 in the second equation

[tex]x - 8 = 10 * (y - 8)[/tex]

[tex]4y - 6 - 8 = 10 * (y - 8)[/tex]

[tex]4y - 14 = 10y - 80[/tex]

Collect Like Terms

[tex]4y - 10y = 14 - 80[/tex]

[tex]-6y = -66[/tex]

Divide through by -6

[tex]y = 11[/tex]

Substitute 11 for y in [tex]x = 4y - 6[/tex]

[tex]x = 4 * 11 - 6[/tex]

[tex]x = 44 - 6[/tex]

[tex]x = 38[/tex]

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