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# Plugging In: Invisible Plugging In - Fractions

Company _X_ sent one third of its stock to store _A_. The remaining stock was equally distributed between stores _B_ and _C_. If stores _A_, _B_, and _C_ sold $$\frac{5}{8}$$, $$\frac{3}{8}$$ and $$\frac{7}{8}$$, respectively, of the stock sent to them, what fraction of the total stock remains unsold?
Incorrect. [[snippet]] This is the fraction of total stock that was sold.
Incorrect. [[snippet]]
Correct. [[snippet]] The invisible variable is Company _X_'s total stock. The company sends $$\frac{1}{3}$$ of the stock to _A_, and the rest is distributed equally between _B_ and _C_, or $$\frac{1}{2}$$ (of the rest) each. The question then presents the fraction of the stock that was sold out of the amount of stock each shop received, and these amounts are given in various fractions, all with a denominator of 8. Multiply the bottoms of the fractions in the problem, >$$3\times 2\times 8=48$$, to find your good number. (There's no need to multiply 8 three times while looking for a good number to __Plug In__, because $$\frac{5}{8}$$, $$\frac{3}{8}$$, and $$\frac{7}{8}$$ are taken independently from different stocks). Store _A_ received $$\frac{1}{3}\times 48=16$$, leaving 32. Stores _B_ and _C_ each received half of 32, or 16. Now begins the real fun: store _A_ sold $$\frac{5}{8}$$ of its stock (10), store _B_ sold $$\frac{3}{8}$$ of its stock (6), and store _C_ sold $$\frac{7}{8}$$ of its stock (14). Combine all the unsold stock from stores _A_, _B_, and _C_, respectively: >$$6+10+2=18$$. The fraction of the unsold stock is $$\frac{18}{48}$$ or $$\frac{3}{8}$$.
Incorrect. [[snippet]]
Incorrect. [[snippet]]
$$\frac{1}{16}$$
$$\frac{1}{8}$$
$$\frac{3}{8}$$
$$\frac{1}{2}$$
$$\frac{5}{8}$$