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Question
Math
Posted 2 months ago

Joseph gave 1/41 / 4 of his candies to Joy and Joy gave 1/51 / 5 of what she got to Tim. If Tim received 2 candies, how many candies did Joseph have originally?
A. 30
B. 20
C. 50
D. 40
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Answer from Sia
Posted 2 months ago
Solution by Steps
step 1
Let xx be the number of candies Joseph originally had. Joseph gave 14\frac{1}{4} of his candies to Joy, so Joy received 14x\frac{1}{4}x candies
step 2
Joy then gave 15\frac{1}{5} of what she received to Tim. Therefore, Tim received 15(14x)=120x\frac{1}{5} \left( \frac{1}{4} x \right) = \frac{1}{20} x candies
step 3
We know that Tim received 2 candies. So, we set up the equation 120x=2\frac{1}{20} x = 2
step 4
To solve for xx, multiply both sides of the equation by 20: x=2×20=40x = 2 \times 20 = 40
Answer
Joseph originally had 40 candies.
Key Concept
Fractional distribution
Explanation
The problem involves understanding how fractions of a quantity are distributed and then working backwards to find the original quantity.

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