Answered

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A merchant, in order to attract customers, increased the price of some of his products by 10% and, at the time of sale, offered a 25% discount. Determine the actual discount given by the merchant.
15%
17.5%
20%
23.5%​

Sagot :

GreatNiclaus

✒️[tex]\large{\mathcal{ANSWER}}[/tex]

[tex]======================[/tex]

  • The actual discount given by this merchant was 17.5%, therefore, we conclude that the correct alternative is the letter B.

•But how do you know this?

  • A very simple way to solve this account is by establishing values, let's say that the initial price of the product is 10 .

The merchant has increased the price by 10%, so the value of the product will be:

[tex] \frac{10}{100} \times \frac{10 }{1} = \frac{100}{100} = \: \boxed{1 real} [/tex]

[tex]10 \: real + 1 \: real = 11 \: real[/tex]

•And this merchant gave a 25% discount on that product.

•A tip: 25% is the same thing as dividing that number by 4:

[tex] \frac{11}{4} = \: \boxed{275} [/tex]

•The value of the product with the 25% discount will be: 10 - 2.75 = 8.25.

|But, notice that this merchant raised the price, so to figure out the real discount, let's use a simple rule of 3, such that:

  • 10 real –––– 100%
  • 825 real –––– x%

• Means through the extremes:

[tex]10x = 825.100 \\ 10x = 825 \\ x = \frac{825}{10} \\ x = 825\%[/tex]

Now, just subtract 100% of this percentage, then:

[tex]100\% - 825\% = 175 \%[/tex]

  • Therefore, the real value of the discount was 17.5%.

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Good studies and I hope I have helped.

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