There are 5 buttons on a headband and 3 buttons on a scarf
let h represent a headband and s represent a scarf, then
14s + 12h = 102 → (1)
14s + 9h = 87 → (2)
(2) - (1) term by term to eliminate the term in s
3h = 15 ( divide both sides by 3 )
h = 5
substitute h = 5 in either (1) or (2) and solve for s
(2) : 14s + 45 = 87 ( subtract 45 from both sides )
14s = 42 ( divide both sides by 14 )
s = 3