College

Look at Mia's work.

[tex]
\[
\begin{aligned}
83+n & =110 \\
83+83+n & =110+83 \\
n & =193
\end{aligned}
\]
[/tex]

What was Mia's error?

A. Mia's work is correct.

B. Mia made an addition error when adding 110 and 83.

C. Mia only needed to add 83 to 110.

D. Mia should have subtracted 83 from both sides of the equation.

Answer :

We start with the equation

[tex]$$83 + n = 110.$$[/tex]

To isolate [tex]$n$[/tex], we need to remove [tex]$83$[/tex] from the left side. The proper operation is to subtract [tex]$83$[/tex] from both sides, as follows:

[tex]$$83 + n - 83 = 110 - 83.$$[/tex]

This simplifies to

[tex]$$n = 27.$$[/tex]

Instead, Mia added [tex]$83$[/tex] to both sides, leading her to write

[tex]$$83 + 83 + n = 110 + 83,$$[/tex]

or

[tex]$$166 + n = 193.$$[/tex]

This manipulation does not cancel out the [tex]$83$[/tex] on the left side. If one mistakenly treats [tex]$193$[/tex] as the value of [tex]$n$[/tex], then it would be an incorrect result.

Thus, the error in Mia's work is that she should have subtracted [tex]$83$[/tex] from both sides of the equation rather than adding [tex]$83$[/tex].

The correct choice is:

[tex]$$\textbf{Mia should have subtracted 83 from both sides of the equation.}$$[/tex]

Other Questions