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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

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Answer

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.

Solution

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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