SOLUTION: 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

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?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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?
.
Let x = number of oranges Leona had at the start
.
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
.
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

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