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

10 years old

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