Dwarf fairy calculation

There were 3 dwarves more than fairies in the forest kingdom. A drought hit the kingdom, and a quarter of the dwarves and one fairy left. The king thus reduced the number of dwarves and fairies in the kingdom to 3. How many fairies and dwarves were there originally in the kingdom?

Final Answer:

t =  4
v =  1

Step-by-step explanation:

t=3+v
t-t/4+v-1=3

t-v = 3
3t+4v = 16

Pivot: Row 1 ↔ Row 2
3t+4v = 16
t-v = 3

Row 2 - 1/3 · Row 1 → Row 2
3t+4v = 16
-2.33v = -2.33


v = -2.33333333/-2.33333333 = 1
t = 16-4v/3 = 16-4 · 1/3 = 4

t = 4
v = 1

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