Which of the following choices can be used to check the answer in this equation?
$205-110=95$
Answer (2)
The problem requires checking the equation 205 − 110 = 95 .
Rewrite the equation as 205 = 110 + 95 .
Check if any of the given choices directly verify this relationship.
Conclude that none of the choices can be used to directly check the answer.
Explanation
Understanding the Problem We are given the equation 205 − 110 = 95 and asked to determine which of the given choices can be used to check if the equation is correct. The key idea here is to understand the relationship between addition and subtraction.
Rewriting the Equation The given equation 205 − 110 = 95 can be rewritten as an addition equation. If we add 110 to both sides of the equation, we get 205 = 110 + 95 . This means that if the original equation is correct, then 110 + 95 must equal 205 .
Analyzing the Choices Now, let's examine the given choices:
205 + 110 = 315 : This equation doesn't directly help us check if 205 − 110 = 95 is correct.
205 + 110 + 95 = 410 : This equation also doesn't directly help us check the original equation.
205 + 95 = 300 : This equation also doesn't directly help us check the original equation.
However, we know that if 205 − 110 = 95 is true, then 205 = 110 + 95 must also be true. We can check if 110 + 95 indeed equals 205 .
Checking the Addition Let's evaluate 110 + 95 . The result of this addition is 205 . This confirms that the original equation 205 − 110 = 95 is correct. However, none of the provided choices directly represent this check. The closest we can get to verifying the equation is by recognizing that 205 = 110 + 95 . We can rearrange this to check if 205 − 95 = 110 , but this is not among the options.
Final Verification and Conclusion Since 205 − 110 = 95 , it means 205 = 110 + 95 . We are looking for an equation among the choices that helps verify this. None of the choices directly show 110 + 95 = 205 . However, we can see that if we subtract 95 from both sides of 205 = 110 + 95 , we get 205 − 95 = 110 . This is not among the choices. If we subtract 110 from both sides of 205 = 110 + 95 , we get 205 − 110 = 95 , which is the original equation. Thus, we are looking for a rearrangement of the original equation that helps us verify it.
However, upon closer inspection, we can see that none of the choices can be used to directly check the answer in the equation.
Examples
When balancing a checkbook, you often use addition to verify subtraction. For example, if your statement shows a starting balance of $205, a withdrawal of $110, and an ending balance of $95, you can verify this by adding the withdrawal amount ($110) to the ending balance ($95). If the sum equals the starting balance ($205), then the subtraction is correct. This principle applies to many real-life scenarios where you need to check calculations involving differences.
To verify the equation 205 − 110 = 95 , we can rewrite it as 205 = 110 + 95 . However, none of the provided choices directly help in checking this relationship, as they do not represent any effective method to verify the original equation.
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