Gavin has 106 pieces of $5 notes and $10 notes. He used 2/3 of the $10 notes and put in another six $5 notes. As a result, the number of $5 notes was fives times the number of $10 notes. What was the total value of the $5 notes Gavin have at first?

Answer 1

if there are f 5's and t 10's, then we know that
f+t = 106
f+6 = 5(1/3 t)
f=64 and t=42
check: 5*14 = 6+64✅
so the 42 $5 notes were worth $210

Answer 2

As x pieces of $5
y pieces of 10 x + y = 106 =>
y = 106 - x (1)
1/3y * 5 = x + 6 (2)
Put (1) into (2)
5/3 (106 - x) = x + 6
5 (106 - x) = 3x + 18
530 - 5x = 3x + 18
8x = 530 - 18 x = 512/8 = 64
64 * 5 = 320

Answer 3

my typo - my bad.
Way to watch, Anonymous.