Pregunta
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1. Calculate the a. 6 is \( 24 \% \) of a number, what is the number? b. If Birr 700 is \( 35 \% \) of Birr \( x \), then what is the value of \( x \) ? c. If \( 15 \% \) of a number is 18 , then what is the number? d. \( 40 \% \) of a number is 110 , what is number? 2. If \( 30 \% \) of a man's salary is Birr 6300 , what is the amount of his full salary? 3. In a class where the number of boys is \( 36 \% \) of the total number of student there are 18 boys, then how many students are there in the class?

Ask by George Klein. in Ethiopia
Feb 24,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

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1. **Calculations:** a. The number is **25**. b. \( x = 2000 \). c. The number is **120**. d. The number is **275**. 2. The man's full salary is **21,000** Birr. 3. There are **50** students in the class.

Solución

Solve the equation by following steps: - step0: Solve for \(x\): \(0.4x=110\) - step1: Divide both sides: \(\frac{0.4x}{0.4}=\frac{110}{0.4}\) - step2: Divide the numbers: \(x=275\) Solve the equation \( 0.36x=18 \). Solve the equation by following steps: - step0: Solve for \(x\): \(0.36x=18\) - step1: Divide both sides: \(\frac{0.36x}{0.36}=\frac{18}{0.36}\) - step2: Divide the numbers: \(x=50\) Solve the equation \( 0.15x=18 \). Solve the equation by following steps: - step0: Solve for \(x\): \(0.15x=18\) - step1: Divide both sides: \(\frac{0.15x}{0.15}=\frac{18}{0.15}\) - step2: Divide the numbers: \(x=120\) Solve the equation \( 0.24x=6 \). Solve the equation by following steps: - step0: Solve for \(x\): \(0.24x=6\) - step1: Divide both sides: \(\frac{0.24x}{0.24}=\frac{6}{0.24}\) - step2: Divide the numbers: \(x=25\) Solve the equation \( 0.35x=700 \). Solve the equation by following steps: - step0: Solve for \(x\): \(0.35x=700\) - step1: Divide both sides: \(\frac{0.35x}{0.35}=\frac{700}{0.35}\) - step2: Divide the numbers: \(x=2000\) Solve the equation \( 0.3x=6300 \). Solve the equation by following steps: - step0: Solve for \(x\): \(0.3x=6300\) - step1: Divide both sides: \(\frac{0.3x}{0.3}=\frac{6300}{0.3}\) - step2: Divide the numbers: \(x=21000\) Here are the detailed solutions for each part of your problem: 1. **Calculating the unknown numbers:** a. **6 is \( 24\% \) of a number, what is the number?** \[ 0.24x = 6 \implies x = \frac{6}{0.24} = 25 \] The number is **25**. b. **If Birr 700 is \( 35\% \) of Birr \( x \), then what is the value of \( x \)?** \[ 0.35x = 700 \implies x = \frac{700}{0.35} = 2000 \] The value of \( x \) is **2000**. c. **If \( 15\% \) of a number is 18, then what is the number?** \[ 0.15x = 18 \implies x = \frac{18}{0.15} = 120 \] The number is **120**. d. **\( 40\% \) of a number is 110, what is the number?** \[ 0.4x = 110 \implies x = \frac{110}{0.4} = 275 \] The number is **275**. 2. **If \( 30\% \) of a man's salary is Birr 6300, what is the amount of his full salary?** \[ 0.3x = 6300 \implies x = \frac{6300}{0.3} = 21000 \] The amount of his full salary is **21000**. 3. **In a class where the number of boys is \( 36\% \) of the total number of students, and there are 18 boys, how many students are there in the class?** \[ 0.36x = 18 \implies x = \frac{18}{0.36} = 50 \] The total number of students in the class is **50**. These calculations provide the answers to all parts of your problem.

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Bonus Knowledge

To find the number that corresponds to \( 6 \) being \( 24\% \), you can set up the equation \( 6 = 0.24x \). Solving gives \( x = \frac{6}{0.24} = 25 \). For the \( Birr 700 \), \( 700 = 0.35x \) leads to \( x = \frac{700}{0.35} = 2000 \). For \( 15\% \) giving \( 18 \), you solve \( 0.15x = 18 \) to find \( x = \frac{18}{0.15} = 120 \). Finally, with \( 40\% \) and \( 110 \), it's \( 0.40x = 110 \) which gives \( x = \frac{110}{0.40} = 275 \). For the man’s salary, if \( 30\% \) is \( 6300 \), set \( 6300 = 0.30s \) and find \( s = \frac{6300}{0.30} = 21000 \). Lastly, knowing \( 36\% \) of the total students equals \( 18 \), use \( 0.36t = 18 \) to find \( t = \frac{18}{0.36} = 50 \). So, the class has \( 50 \) students in total! Isn’t math magical?

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