SOLUTION: On Saturday morning, Mr. Brown often goes to the public market for fresh produce. He spent 1/4 of his money on vegetables, 1/2 of the remaining money on fruit, and 1/3 of the remai

Question 935409: On Saturday morning, Mr. Brown often goes to the public market for fresh produce. He spent 1/4 of his money on vegetables, 1/2 of the remaining money on fruit, and 1/3 of the remaining money on cheese Mr. Brown had $12 when he finished. Work backwards to find how much money he had when he started.
Found 3 solutions by TimothyLamb, josgarithmetic, MathTherapy:
Answer by TimothyLamb(4379)   (Show Source): You can put this solution on YOUR website!
x = original amount
y = amount spent on vegetables
z = amount spent on fruit
u = amount spent on cheese
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y = x/4
z = (x - y)/2
u = (x - y - z)/3
x - y - z - u = 12
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put the system of linear equations into standard form
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x - 4y = 0
x - y - 2z = 0
x - y - z - 3u = 0
x - y - z - u = 12
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copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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solution:
x = original amount = 48
y = amount spent on vegetables = 12
z = amount spent on fruit = 18
u = amount spent on cheese = 6
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Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Working forward is easier (for me, at least).

Let p be the original amount of money.

Bought vegetables. Money remaining, .

Bought fruit. Money remaining, .

Bought cheese, last, using of , so what remains is , which
is the quantity, $12.

-

, original amount of money.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

On Saturday morning, Mr. Brown often goes to the public market for fresh produce. He spent 1/4 of his money on vegetables, 1/2 of the remaining money on fruit, and 1/3 of the remaining money on cheese Mr. Brown had $12 when he finished. Work backwards to find how much money he had when he started.

Before he was left with $12, he had spent on cheese
Therefore, before he bought cheese, he had , or $18
Since he spent � of remainder on fruit, before he bought fruit, he had , or $36
Since he spent � of remainder on vegetables, before he bought vegetables, he had , or $
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