Gary tried to solve an equation:
[tex]\begin{array}{rlr}
\frac{e}{4} & =2.5 & \\
\frac{e}{4} \cdot 4 & =2.5 \cdot 4 & \text { Setting up } \\
e & =8 & \text { Calculating }
\end{array}[/tex]
Where did Gary make his first mistake?
A. Setting up
B. Calculating
C. Gary correctly solved the equation.
Answer (2)
The initial equation is 4 e = 2.5 .
Multiply both sides by 4: 4 e × 4 = 2.5 × 4 .
Calculate 2.5 × 4 = 10 .
Gary's mistake was calculating e = 8 instead of e = 10 , so the answer is C a l c u l a t in g .
Explanation
Analyzing Gary's Solution Let's analyze Gary's steps to identify where he made a mistake.
Step 1: The initial equation is 4 e = 2.5 .
Step 2: Gary multiplies both sides of the equation by 4 to isolate e : 4 e ⋅ 4 = 2.5 ⋅ 4 .
Step 3: Gary calculates the result and states that e = 8 .
Checking the Calculation Now, let's verify Gary's calculation. We need to compute 2.5 × 4 .
2.5 × 4 = 10
Identifying the Mistake Comparing our calculation with Gary's result, we see that Gary incorrectly calculated 2.5 × 4 as 8, when the correct result is 10. Therefore, Gary's mistake lies in the calculation step.
Correct Solution Gary made a mistake in the 'Calculating' step. The correct calculation should be:
4 e = 2.5 4 e ⋅ 4 = 2.5 ⋅ 4 e = 10
Examples
Understanding how to solve simple equations like this is crucial in many real-life situations. For example, if you want to split a bill of $25 among 4 friends, you would use the equation 4 x = 25 to find the total bill amount x . Similarly, if you know that a quarter of your monthly allowance is $50, you can use the equation 4 a = 50 to calculate your total monthly allowance a . These basic algebraic skills are fundamental for managing finances and solving everyday problems.
Gary made a mistake in the calculating step when he stated that e = 8 . The correct calculation of 2.5 ⋅ 4 equals 10, so the correct result is e = 10 . Therefore, the answer is option B: Calculating.
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