A father is four times as old as his daughter. In 6 years, he will be three times as old as she is. How old is the daughter now?

Answer 1

The daughter is #12# years old.

We shall consider the father´s age as #x# and the daughter´s age as #y#. From the details, we can write these two equations:

#x=4y# #x+6=3(y+6)#

Simplify the second equation by opening the brackets.

#x+6=3y+18#

Subtract #6# from both sides.

#x=3y+12#

Using the value of #x# from the first equation, substitute #x# in the simplified second equation with #color(red)(4y)#.

#x=3y+12#

#color(red)(4y)=3y+12#

Subtract #3y# from both sides.

#y=12#

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Answer 2

Abigail Allen

Let ( F ) represent the father's current age and ( D ) represent the daughter's current age.

Given: [ F = 4D ] [ F + 6 = 3(D + 6) ]

Using the first equation, substitute ( F ) in the second equation: [ 4D + 6 = 3(D + 6) ]

Solve for ( D ): [ 4D + 6 = 3D + 18 ] [ 4D - 3D = 18 - 6 ] [ D = 12 ]

So, the daughter is currently 12 years old.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.