Let's go through Chris's steps and identify where the first error occurred, then correct the steps and find the final answer.
### Chris's Steps Review:
1. Chris's Step 1: She begins with the expression:
[tex]\[
2(-20) + 3\left[\frac{5}{4}(-20)\right] + 5\left[\frac{2}{5}(50)\right] + 4(50)
\][/tex]
Evaluating each term:
[tex]\[
2(-20) = -40
\][/tex]
[tex]\[
3\left[\frac{5}{4}(-20)\right] = 3 \cdot (-25) = -75
\][/tex]
[tex]\[
5\left[\frac{2}{5}(50)\right] = 5 \cdot 20 = 100
\][/tex]
[tex]\[
4(50) = 200
\][/tex]
So Step 1 should be:
[tex]\[
-40 + (-75) + 100 + 200
\][/tex]
Chris did this step correctly.
2. Chris's Step 2: Combining terms incorrectly:
[tex]\[
(3 + 2)(-20 + (-25)) + (5 + 4)(20 + 50)
\][/tex]
This is incorrect because she grouped and combined the terms incorrectly, changing the operations and not following the order of operations. Her mistake is here.
### Correct Steps:
Let's correct Chris's process:
Step 1: Evaluate each term separately:
[tex]\[
2(-20) = -40
\][/tex]
[tex]\[
3\left[\frac{5}{4}(-20)\right] = 3 \cdot (-25) = -75
\][/tex]
[tex]\[
5\left[\frac{2}{5}(50)\right] = 5 \cdot 20 = 100
\][/tex]
[tex]\[
4(50) = 200
\][/tex]
Step 2: Sum the evaluated terms:
[tex]\[
-40 + (-75) + 100 + 200
\][/tex]
Step 3: Perform the addition step-by-step:
[tex]\[
-40 + (-75) = -115
\][/tex]
[tex]\[
-115 + 100 = -15
\][/tex]
[tex]\[
-15 + 200 = 185
\][/tex]
The final answer is:
[tex]\[
185
\][/tex]
So the final corrected answer for the expression [tex]\(2(-20) + 3\left[\frac{5}{4}(-20)\right] + 5\left[\frac{2}{5}(50)\right] + 4(50)\)[/tex] is [tex]\(185\)[/tex].
