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What does "a profit of 80 percent on its buy-back price" mean?

A clock store sold a certain clock to a collector for $20$ percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at $50$ percent of what the collector had paid. The shop then sold the clock again at a profit of $80$ percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $100$, for how much did the shop sell the clock the second time?

There's the initial obtain, the first sale, the first buy-back, then the last sale.

1. Obtain an item worth $x$
2. Collect $20%$ on the value of $x$
3. Collect $10%$ on the value of $x$ because you gained half of what they paid
4. I have no idea what this means. 

Is this right?

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  • $\begingroup$ The shop sold the object then bought it back. The "buy back price" is the price at which they bought it back. They then sold it for a second time, at $80\%$ more than that buy back price. Thus, if the buy back price was $\$100$, they sold it (the second time) for $\$180$. $\endgroup$
    – lulu
    Commented Feb 3, 2023 at 16:11
  • $\begingroup$ Should say, personally I don't find those hints (if that's what they are) terribly helpful. I suggest starting by declaring a variable, let's say $P$, for the initial purchase price, then writing down all the given information in terms of $P$. $\endgroup$
    – lulu
    Commented Feb 3, 2023 at 16:13
  • $\begingroup$ Does this clock problem need an instant answer ? $\endgroup$
    – Jean Marie
    Commented Feb 3, 2023 at 18:52

1 Answer 1

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The store bought the clock for $\$x$, sold it for $\$\frac{6x}5$ and bought it again for $\$\frac{3x}5$.

$x-\frac{3x}5= \frac{2x}5=100$ means $x=250$.

Buy-back price is $\$150$.

$150\cdot\frac95 = 270$.

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  • $\begingroup$ Why does $x$ and $\dfrac{3x}{5}$ have opposite signs? @JMP $\endgroup$
    – user685056
    Commented Feb 3, 2023 at 21:41
  • $\begingroup$ @user1109365 The problem says that the difference between the clock's original cost and the clock's buy-back price was $\$100$. $\endgroup$ Commented Feb 3, 2023 at 23:57

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