2530.52 – Defined Operation 4; Do Composition

Tags:Problem Set 9GeometrySymbol-Pushing

Here are two made-up operations, g and r.

If 10 g = 16, 100 g = 196, and 4 g = 4; and also if 12 r = 5, 300 r = 101, 30 r = 11,

then what is n if n g r = 9?

(Notation: n g r means we do g to n and then r to that. So n g r means (ng)r .)

Solution

g: 10 → 16 ,&nbsp 100 → 196 ,&nbsp 4 → 4 , &nbsp x → 2x – 4

r: 12 → 5 ,&nbsp 300 → 101 ,&nbsp 30 → 11 ,&nbsp x → x/3 + 1

g r: n (2n - 4)/3 + 1 = 9

(2n – 4)/3 + 1 = 9

2n – 4 = 24

n = 14

Check: 14 g r = (2*14 – 4)/3 + 1 = 24/3 + 1 = 9