Joaquin is four more than half Marjorie's age. Marjorie is also 32 less than three times Joaquin's age. How old is Marjorie, in years?

Joaquin = 4 + Marjorie

Marjorie = 3 * Joaquin - 32

Let's say Joaquin is x.

Let's say Marjorie is y.

x=4+y

y=3x-32

y=x-4

y=3x-32

x-4=3x-32 (Subsititute)

-4=2x-32

28 = 2x

x = 14

In other words, Joaquin is 14 years old.

Now, substitute:

x=4+y; x=14

14 = 4+y

y=10

So, Marjorie is 10 years old.

In conclusion, Joaquin is 14 years old and Marjorie is 10 years old.