Joseph gave $1 / 4$ of his candies to Joy and Joy gave $1 / 5$ 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

Question

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Let $x$ be the number of candies Joseph originally had. Joseph gave $\frac{1}{4}$ of his candies to Joy, so Joy received $\frac{1}{4}x$ candies. ‖ ‖ step 2 ⋮ Joy then gave $\frac{1}{5}$ of what she received to Tim. Therefore, Tim received $\frac{1}{5} \left( \frac{1}{4} x ight) = \frac{1}{20} x$ candies. ‖ ‖ step 3 ⋮ We know that Tim received 2 candies. So, we set up the equation $\frac{1}{20} x = 2$. ‖ ‖ step 4 ⋮ To solve for $x$, multiply both sides of the equation by 20: $x = 2 imes 20 = 40$. ‖ ∻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.⚹◊What is the total number of candies that Joy received from Joseph?⍭ Generate me a similar question◊

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