Question

check the following addition. if the answer is incorrect, find the correct answer.

$$\
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$$

select the correct choice below and, if necessary, fill the answer box to complete your choice.
a. the answer 778 is correct because re - adding from bottom to top gives the same answer.
b. the answer 778 is incorrect because re - adding from bottom to top gives the correct answer. \boxed{}

Explanation:

Step1: Add the numbers correctly

First, identify the numbers to add: \(78\), \(278\), \(225\), and \(285\). Let's add them step by step.
First, add \(78 + 278\). \(78+278 = 356\).
Then, add \(356 + 225\). \(356+225 = 581\).
Then, add \(581 + 285\). \(581+285 = 866\).
Wait, maybe the original problem is a vertical addition: let's check the vertical addition as presented. The numbers are \(78\), \(278\), \(225\), \(285\) (maybe the first number is \(78\), then \(278\), \(225\), \(285\) stacked for addition). Wait, the original addition shown is:
\[

$$\begin{align*} &\ \ \ 78\\ &\ 278\\ &\ 225\\ +&\ 285\\ \hline \end{align*}$$

\]
Wait, maybe I misread. Let's add the digits column by column.
Units place: \(8 + 8 + 5 + 5 = 26\). Write down \(6\), carry over \(2\).
Tens place: \(7 + 7 + 2 + 8 + 2\) (carry) \(= 26\). Write down \(6\), carry over \(2\).
Hundreds place: \(0 + 2 + 2 + 2 + 2\) (carry) \(= 8\). Wait, no, maybe the first number is \(78\) (two digits), \(278\) (three digits), \(225\) (three digits), \(285\) (three digits). So aligning by place value:
Units: \(8 + 8 + 5 + 5 = 26\) → units digit \(6\), carry \(2\)
Tens: \(7 + 7 + 2 + 8 + 2\) (carry) \(= 26\) → tens digit \(6\), carry \(2\)
Hundreds: \(0 + 2 + 2 + 2 + 2\) (carry) \(= 8\)? No, wait \(78\) is two digits, so hundreds place is \(0\), \(278\) has \(2\) in hundreds, \(225\) has \(2\), \(285\) has \(2\). So hundreds: \(0 + 2 + 2 + 2 = 6\) plus carry \(2\) → \(8\). Wait, no, my initial addition was wrong. Wait, let's add \(78 + 278 = 356\), \(356 + 225 = 581\), \(581 + 285 = 866\). So the correct sum is \(866\), not \(778\). So the answer \(778\) is incorrect. So option B is correct, and the correct answer is \(866\).

Step2: Evaluate the options

Option A says the answer \(778\) is correct, but our calculation shows it's wrong. Option B says it's incorrect, which is true. Then we need to find the correct answer, which is \(866\).

Answer:

B. The answer 778 is incorrect because re-adding from bottom to top gives the correct answer (correct answer is 866)