Betty is three times as old as her son now. In 12 years, Betty's age will be three years less than twice her son's age. How old is Betty's son now?

Betty is 27. Her son is 9.

Step-by-step explanation:

We will use b to represent Betty's age. We will use s to represent her son's age.

This year:

b = 3s

In 12 years' time:

b + 12 = 2(s + 12) - 3

b + 12 = 2s + 24 - 3

b + 12 = 2s + 21

b = 2s + 9

We know that b = 3s, so we can substitute this value into our equation.

3s = 2s + 9

s = 9

b = 3 x 9

b = 27

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.