A store marks up a picture frame 70% from its wholesale price. In a clearance sale, the price is discounted by 30%. The sale price is $34.51. What was the wholesale price of the picture frame?
Question:
A store marks up a picture frame {eq}70 % {/eq} from its wholesale price. In a clearance sale, the price is discounted by {eq}30 % {/eq}. The sale price is {eq}$34.51 {/eq}. What was the wholesale price of the picture frame?
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CarlaApril 1, 2023 в 19:37
Let's use algebra to solve for the wholesale price (let's call it "w"). We know that the store marked up the wholesale price by 70%, meaning they sold it for 1.7 times the wholesale price:
{eq}1.7w {/eq}
We also know that the clearance sale discounted the price by 30%, meaning the sale price is 70% of the marked-up price:
{eq}0.7(1.7w) = 1.19w {/eq}
Finally, we know that the sale price was $34.51, so we can set up an equation:
{eq}1.19w = 34.51 {/eq}
Solving for w, we get:
{eq}w = \frac{34.51}{1.19} \approx 28.97 {/eq}
Therefore, the wholesale price of the picture frame was \approx imately $28.97.
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