Si el $20 x \%$ del $15 \%$ de $\frac{1}{5}$ del $20 \%$ de 1200 es igual a 36. Halla el valor de $M=\sqrt{x}+10$
Answer (2)
Translate the problem into an equation: 100 20 x × 100 15 × 5 1 × 100 20 × 1200 = 36 .
Simplify the equation to isolate x .
Solve for x : x = 25 .
Calculate M = x + 10 = 25 + 10 = 15 . The final answer is 15 .
Explanation
Problem Analysis We are given that 20 x % of 15% of 5 1 of 20% of 1200 is equal to 36. Our goal is to find the value of M = x + 10 . First, we need to translate the given information into an equation and solve for x .
Equation Setup Let's express the given information as an equation: 100 20 x × 100 15 × 5 1 × 100 20 × 1200 = 36
Simplifying the Equation Now, let's simplify the equation. We can rewrite the equation as: 100 20 x × 100 15 × 5 1 × 100 20 × 1200 = 36 First, let's calculate the product of the constants: 100 15 × 5 1 × 100 20 × 1200 = 100 × 5 × 100 15 × 1 × 20 × 1200 = 50000 360000 = 7.2 So the equation becomes: 100 20 x × 7.2 = 36
Solving for x Now, we can further simplify the equation: 100 20 x × 7.2 = 36 5 x × 7.2 = 36 x × 5 7.2 = 36 x = 5 7.2 36 = 7.2 36 × 5 = 7.2 180 = 25
Calculating M Now that we have found the value of x , we can calculate M = x + 10 :
M = 25 + 10 = 5 + 10 = 15
Final Answer Therefore, the value of M is 15.
Examples
Understanding percentages is crucial in everyday life, from calculating discounts while shopping to determining interest rates on loans. For instance, if a store offers a 20% discount on an item originally priced at $100, you would calculate 20% of $100, which is $20, and then subtract that from the original price to find the sale price of $80. This problem demonstrates how multiple percentages applied sequentially can affect a final value, a concept often used in financial calculations, such as determining the overall return on an investment after accounting for various fees and taxes. By mastering these calculations, you can make informed decisions about your finances and spending habits.
To find the value of M, we first set up an equation based on the problem statement, finding that x equals 25. This leads us to calculate M as 15. Therefore, M is 15.
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