# What's the fourth step in this word problem about a pawn-shop?

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?

• 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$\$180$.
– lulu
Commented Feb 3, 2023 at 16:11
• 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 $P$.
– lulu
Commented Feb 3, 2023 at 16:13
• Does this clock problem need an instant answer ? Commented Feb 3, 2023 at 18:52

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 $$\150$$.
$$150\cdot\frac95 = 270$$.
• Why does $x$ and $\dfrac{3x}{5}$ have opposite signs? @JMP
• @user1109365 The problem says that the difference between the clock's original cost and the clock's buy-back price was $\$100\$. Commented Feb 3, 2023 at 23:57