Answered

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Mia tried to solve an equation step by step.

[tex]\[
\begin{aligned}
0.1 t - 3 & = 5 \\
0.1 t & = 8 \quad \text{Step 1} \\
t & = 80 \quad \text{Step 2}
\end{aligned}
\][/tex]

Find Mia's mistake.

Choose one answer:
A. Step 1
B. Step 2
C. Mia did not make a mistake.

Sagot :

GinnyAnswer
Let's analyze Mia's solution step-by-step to find any possible mistakes:

Given Equation:
[tex]\[ 0.1t - 3 = 5 \][/tex]

Step 1: Adding 3 to both sides
[tex]\[ 0.1t - 3 + 3 = 5 + 3 \][/tex]
[tex]\[ 0.1t = 8 \][/tex]
Here's where the mistake is. Instead of concluding that [tex]\(0.1t = 2\)[/tex], it should actually be [tex]\( 0.1t = 8 \)[/tex].

Step 2: Solving for [tex]\( t \)[/tex] by dividing both sides by 0.1
[tex]\[ t = \frac{8}{0.1} \][/tex]
[tex]\[ t = 80 \][/tex]
Therefore, [tex]\( t \)[/tex] should be 80, not 20.

So, Mia's mistake lies in Step 1. The correct solution step-by-step should be:
1. Starting from the equation:
[tex]\[ 0.1t - 3 = 5 \][/tex]
2. Adding 3 to both sides:
[tex]\[ 0.1t = 8 \][/tex]
3. Solving for [tex]\( t \)[/tex]:
[tex]\[ t = \frac{8}{0.1} = 80 \][/tex]

In conclusion, Mia's mistake occurred in Step 1. Therefore, the correct answer is:

(A) Step 1
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