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Mr. Choo had some blue and red stickers at first.
(a) If he gives out 4 blue stickers and 5 red stickers everyday, he will be left with 24 blue stickers
and 0 red sticker.
(b) If he gives out 9 blue stickers and 4 red stickers everyday for the same number of days as before,
he will be left with 1/3 as many red stickers as blue stickers.
How many blue stickers did he have at first?
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Let R be the number of red stickers; B be the number of blue stickers and n be the number of days.
Then from statement (a)
R = 5n (1)
B = 4n + 24. (2)
From statement (b), after n days, the number of blue stickers will be B-9n = (4n+24)-9n = 24-5n,
while the number of red stickers will be 5n-4n = n.
Then, according to statement (b), we have this equation for unknown "n"
3n = 24-5n (3)
From equation (3), we find
3n + 5n = 24 ---> 8n = 24 ---> n = 24/8 = 3 (days).
Hence, the number of blue stickers initially, according to formula (2), was
B = 4n + 24 = 4*3 + 24 = 12 + 24 = 36.
ANSWERE. The number of blue stickers was 36 at first.
Solved.
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The strategy is as follows.
(1) Introduce n = the number of days.
(2) From the first statement, deduce expressions for red sticks and for blue sticks separately.
(3) From the second statement, deduce expressions for remaining sticks.
(4) Then from statement (b) make an equation and solve it for the number of days.
(5) Having the number of days, restore the unknown number of blue sticks.
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