Select the correct answer.
The sum of two numbers is -18. If the first number is 10, which equation represents this situation, and what is the second number?
A. The equation that represents this situation is $10-x=-18$. The second number is 28.
B. The equation that represents this situation is $10+x=-18$. The second number is -28.
C. The equation that represents this situation is $x-10=-18$. The second number is -8.
D. The equation that represents this situation is $-10+x=-18$. The second number is -8.
Answer (2)
We define the second number as x .
We form the equation 10 + x = − 18 .
We solve for x by subtracting 10 from both sides: x = − 18 − 10 = − 28 .
The second number is − 28 .
Explanation
Problem Analysis Let's analyze the problem. We are given that the sum of two numbers is -18, and the first number is 10. We need to find the equation that represents this situation and the value of the second number.
Forming the Equation Let the second number be x . The equation representing the sum of the two numbers is: 10 + x = − 18
Solving for x To solve for x , we subtract 10 from both sides of the equation: 10 + x − 10 = − 18 − 10 x = − 28
Verification Now, let's check our answer. The sum of the two numbers should be -18. So, 10 + ( − 28 ) = − 18 , which is correct.
Selecting the Correct Option Comparing our equation 10 + x = − 18 and the value of the second number x = − 28 with the given options, we find that option B matches our solution.
Final Answer Therefore, the correct answer is: The equation that represents this situation is 10 + x = − 18 . The second number is -28.
Examples
Imagine you're managing your finances. You started with $10 in your account, and after some transactions, your balance is egative $18. This problem helps you determine how much money you spent (or lost) during those transactions. By setting up the equation 10 + x = − 18 , where x is the amount spent, you can solve for x to find out exactly how much you spent to reach the final balance. This is a practical application of solving linear equations in everyday life.
The correct equation representing the situation is 10 + x = − 18 , which leads to the second number being -28. Therefore, option B is the correct answer. I verified that the solution is accurate by checking the sum of the two numbers.
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