Question

1. A merchant sets the selling price of an article 40% above what it cost him. Then, seeing it did not sell, he decided to reduce the figure by 15%. The final selling price was $8.65. What did the article originally cost?​

Answer 1

Answer: 7.27 dollars

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Work Shown:

x = original cost (in dollars)

1.40x = increasing the cost by 40%

0.85*1.40x = decreasing the previous cost (1.40x) by 15%

Notice how a decrease of 15% means you pay the remaining 85% of the price, which is where the 0.85 comes from.

The expression 0.85*1.40x simplifies to 1.19x after multiplying the 0.85 and 1.40

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The expression 1.19x is the final cost after the increase of 40% and the decrease of 15%

Set this equal to 8.65 and solve for x

1.19x = 8.65

x = 8.65/1.19

x = 7.2689075630252 which is approximate

x = 7.27 dollars

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Let's check the answer

x = 7.27

1.40x = 1.40*7.27 = 10.178 = 10.18

After an increase of 40%, the cost is now $10.18

Now decrease it by 15%

discount = 15% of 10.18 = 0.15*10.18 = 1.527 = 1.53

The customer saves $1.53 and the final price is 10.18-1.53 = 8.65

So everything works out as we expect. The answer is confirmed.