Let the total number of stickers = x
Stickers given to neighbor = ²/₅ x
Stickers given to sister = ⁵/₉ (⁵/₅ x - ²/₅ x) = ⁵/₉ (³/₅x) ⇒ ¹/₃ x
Stickers left = 80
Equation:
x = ²/₅ x + ¹/₃ x + 80
LCM: (3)(5) ⇒ Multiply each term by LCM, then simplify.
(3)(5)x = (3)(5) ²/₅ x + (3)(5) ¹/₃ x + (3)(5) 80
15x = 6x + 5x + 1,200
15x = 11x + 1,200
15x - 11x = 1,200
4x = 1,200
4x/4 = 1,200/4
x = 300
ANSWER: There were 300 stickers.
Check:
Stickers given to neighbor: ²/₅ (300) = 120 stickers
Stickers given to sister: ⁵/₉ (300-120) = ⁵/₉ (180) = 100 stickers
Stickers left = 80 stickers
Add the stickers:
120 + 100 + 80 = 300
300 = 300
