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The sum of three numbers is 95 . The first number is 7 less than the third. The second number is 4 times the third. What are the numbers? First number:

Ask by Garrett Ortiz. in the United States
Jan 23,2025

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Answer

The first number is 10.

Solution

Let's solve the problem step by step to find the **first number**. **Given:** 1. The sum of three numbers is 95. 2. The first number is 7 less than the third number. 3. The second number is 4 times the third number. **Let's define the numbers:** - Let the **third number** be \( z \). - Then, the **first number** \( x = z - 7 \). - The **second number** \( y = 4z \). **Setting up the equation:** \[ x + y + z = 95 \] \[ (z - 7) + 4z + z = 95 \] \[ 6z - 7 = 95 \] \[ 6z = 102 \] \[ z = 17 \] **Now, find the first number:** \[ x = z - 7 = 17 - 7 = 10 \] **Answer:** - **First number:** **10**

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The Deep Dive

Let the third number be \( x \). Then, the first number can be expressed as \( x - 7 \) and the second number as \( 4x \). According to the problem, the equation would be: \[ (x - 7) + 4x + x = 95 \] Combining like terms gives us: \[ 6x - 7 = 95 \] Adding 7 to both sides results in: \[ 6x = 102 \] Dividing both sides by 6 gives: \[ x = 17 \] Now we can find the first and second numbers: - First number: \( x - 7 = 17 - 7 = 10 \) - Second number: \( 4x = 4 \times 17 = 68 \) Thus, the three numbers are: First number: 10, Second number: 68, Third number: 17. Need more math wizardry? The world of numbers is like a thrilling mystery story! Each equation is a clue, revealing the secrets of the digits. You can surprise your friends with your math prowess and share this clever approach to problem-solving — who knew math could be so fun? Want to explore similar mathematical puzzles? You can find various brain-teasers and challenges in books about recreational mathematics or puzzle websites! These often include problems ranging from beginner to advanced levels, promising a delightful journey through logical reasoning and number play.

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