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Chapter 42: Chapter 42

Problem 1202

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The sum of two numbers is 24 ; one number is 3 more than twice the other. Find the numbers.

Short Answer

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The two numbers are \(x = 17\) and \(y = 7\).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Define the variables and set up the equations

Let x be the first number and y be the second number. We are given the following information: 1. The sum of the two numbers is 24: \(x + y = 24\) 2. One number is 3 more than twice the other: We can write this as: \(x = 2y + 3\) Now we have a system of two linear equations with two variables: 1. \(x + y = 24\) 2. \(x = 2y + 3\)

Step 2: Solve the system of equations

To solve this system, we can use the substitution method. Since we are given that \(x = 2y + 3\), we can substitute this expression for x in the first equation: \((2y + 3) + y = 24\) Now, we can solve for y: \(3y + 3 = 24\) Subtract 3 from both sides: \(3y = 21\) Now, divide by 3 to find the value of y: \(y = 7\) Now that we have the value of y, we can find the value of x from the second equation: \(x = 2y + 3\) Substitute the value of y: \(x = 2(7) + 3\) Calculate x: \(x = 14 + 3\) So, x = 17

Step 3: State the answer

The two numbers are x = 17 and y = 7.

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