# Daniel had some stickers. he gave 2/5 of his stickers to his neighbor and 5/9 of the remainder to his sister. if he had 80 stickers left, how many stickers did he have at first?

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by Abby0008

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by Abby0008

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Stickers given to neighbor =

Stickers given to sister = ⁵/₉ (⁵/₅ x - ²/₅ x) = ⁵/₉ (³/₅x) ⇒

Stickers left =

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

Check:

Stickers given to neighbor: ²/₅ (300) =

Stickers given to sister: ⁵/₉ (300-120) = ⁵/₉ (180) =

Stickers left =

Add the stickers:

120 + 100 + 80 = 300

300 = 300