Question

Dina's mother is four times older than Dina. Dina is 35 years younger than her father. Dina's father was 5 years older than Dina's mother when Dina was born. How old is Dina now?

Answer 1

Answer:

10 years old

Step-by-step explanation:

Let m = mother's age

Let f = father's age

Let d = Dina's age

m = 4d               d = f-35                f = m+5

Substitute the middle equation in to the first equation

m = 4(f - 35) Use the distributive property

m = 4f - 140 subtract 4f from both sides

*m -4f = -140

In equation 3 above, subtract m from both sides  to get

f = m+5

f - m = 5  rearrange so that the  m term is first

*-m + f = 5  

Now add the equations together that have *

m -4f = -140

-m + f = 5

     -3f = -135  Divide both sides by -3

f = 45  This is the father's age.  To find Dina's age, plug 45 into the second equation above:

d = f -35

d = 45 -35

d = 10.

To find the mom's age, use the third equation:

f = m+5

45 = m + 5

40 = m

You can check this by plugging the answers you found and you can see that all three equations are solved.

m = 4d                        d = f - 35                 f = m + 5

40 = 4(10)                    10 = 45 - 35            45 = 40 + 5

40 = 40                       10 = 10                     45 = 45