Question

A father is four times as old as his daughter. In 8 years, he will be three times as old as she is. How old is the daughter now

Answer 1

Answer:

16 years old

Step-by-step explanation:

Let "x" represent the daughter's age and "y" represent the father's age. We can use this information to set up two equations...

$4x=y$

$3(x+8)=y+8$

Please note we are only adding "8" because the question states "In 8 years"

We can solve this system of equations using the substitution method. In this case, we can substitute "4x" for "y".

$3(x+8)=4x+8$

Distribute the 3 to each term in the parentheses:

$3(x)+3(8)=4x+8\\3x+24=4x+8$

Subtract 3x from both sides:

$24=x+8$

Subtract 8 from both sides:

$x=16$

The daughter is 16 years old now.

CHECK THE SOLUTION:

Right now:

Daughter - 16

Dad - 64

$64\div 16=4\rightarrow Correct!$

8 years:

Daughter - 24

Dad - 72

$72\div 24=3\rightarrow Correct!$

Therefore we can conclude that the daughter is 16 years old.

Answer 2

Answer:

The daughter is 16 and the father is 64

Step-by-step explanation:

f=father

d=daughter

f = 4d

f+8 = 3(d+8)

solving-

d=16

f=64