Question

I need this ASAP! When David was asked how old he was, he said: "I'm three times younger than my dad, but twice as old as Rebecca." Then little Rebecca ran up to him and declared "I am 30 years younger than my dad." How old is David?

Answer 1

David is 12 years old.

Explanation:

Let r = Rebecca's age

Let d = David's age

let p = Dad's age

David is 3 times as younger than his dad:

d =
`(p)/(3)`

David is 2 times older than Rebecca:

d = 2r

Rebecca is 30 years younger than the dad:

r = p-30

All three equations can be solved by a system

2r =
`(p)/(3)`

r = p-30

multiplying r = p-30 by negative 2 and adding it to 2r =
`(p)/(3)`

0 = (-2p + p/3) + 60

multiplying new equation by 3

0 = (-6p + p) + 180

5p = 180

p = 36

d = 36/3 = 12