Question

Mary tried to evaluate an expression. Here is her work:
(3+73)–32+22
=
(103)–32+22 Step 1
=
30–32+22 Step 2
=
30–9+4 Step 3
=
21+4 Step 4
=
25 Step 5
Is Mary's work correct?

Answer 1

Let's evaluate Mary's expression step by step to check her work:

The original expression is:
\[
(3 + 73) - 32 + 22
\]

**Step 1: Evaluate \(3 + 73\)**
\[
3 + 73 = 76
\]
So, the expression becomes:
\[
76 - 32 + 22
\]

**Step 2: Calculate \(76 - 32\)**
\[
76 - 32 = 44
\]
Now the expression is:
\[
44 + 22
\]

**Step 3: Add \(44 + 22\)**
\[
44 + 22 = 66
\]

Thus, the final result of the expression \( (3 + 73) - 32 + 22 \) is \( 66 \).

Now, let's compare this with Mary's work:

- **Step 1:** \( 3 + 73 = 76\) (correct)
- **Step 2:** Her claim that \( (103) - 32 + 22 = 30 - 32 + 22\) is incorrect. \(76 - 32 = 44\), not \(30\).
- Hence, the rest of her steps become irrelevant as the calculations are based on incorrect results.

**Conclusion:** Mary's work is incorrect, and the correct answer to the expression \( (3 + 73) - 32 + 22 \) is \( 66 \).