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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?

Sagot :

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



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