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Chapter 42: Chapter 42

Problem 1200

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The sum of two numbers is 23 . One of the numbers is 7 more than the other number. What are the numbers?

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The two numbers are 15 and 8.
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: 1. Define the variables

Let x be the first number and y be the second number.

Step 2: 2. Write the equations

We are given two pieces of information: 1) The sum of the numbers is 23: \(x + y = 23\) 2) One number is 7 more than the other: \(x = y + 7\)

Step 3: 3. Solve the system of equations

To solve the system, we can use the method of substitution. Since we know that \(x = y + 7\), we can substitute this expression for x in the first equation. So we get: \[(y+7)+y = 23\]

Step 4: 4. Solve for y

Now we solve the equation for y: \begin{align*} 2y + 7 &= 23 \\ 2y &= 16 \\ y &= 8 \end{align*}

Step 5: 5. Substitute y to find x

Now that we have the value for y, we can substitute it into the equation we found for x to find its value: \begin{align*} x &= y + 7 \\ x &= 8 + 7 \\ x &= 15 \end{align*}

Step 6: 6. State the solution

The two numbers are 15 and 8.

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