Question 156556
Leona set up a fruit stand to sell some of her crop of oranges. The first person who cam by bought 1/3 of her oranges. The second person bought 4. The third person then bought 1/4 of remaining oranges. Leona took the last 15 oranges home and made orange juice. Ho many oranges did leona have when she set up the fruit stand?
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Let x = number of oranges Leona had at the start
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Accounting for all the oranges (total oranges):
"first person who cam by bought 1/3 of her oranges" = (1/3)x
"The second person bought 4" = 4
"The third person then bought 1/4 of remaining oranges" = (1/4)[x-(1/3)x - 4]
"Leona took the last 15 oranges home" = 15
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x = (1/3)x + 4 + (1/4)[x-(1/3)x - 4] + 15
x = x/3 + 4 + (1/4)[x- x/3 - 4] + 15
multiplying both sides by 12 (to get rid of all denominators):
12x = 4x + 48 + 3[x- x/3 - 4] + 180
12x = 4x + 48 + [3x- x - 12] + 180
12x = 4x + 48 + 3x - x - 12 + 180
grouping:
12x = (4x + 3x - x) + (48 - 12 + 180)
12x = (6x) + (216)
12x = 6x + 216
6x = 216
x = 36