- Evaluate the target expression \(4.2 + 15 \times (8.6 - 5)\) to get \(4.2 + 54 = 58.2\).
- Evaluate each option:
- Option A: \(4.2 + 15 \times 3.6 = 58.2\)
- Option B: \(19.2 \times 3.6 = 69.12\)
- Option C: \(4.2 + 54 = 58.2\)
- Option D: \(4.2 + 15 \times 8.6 - 5 = 128.2\)
- Option E: \(19.2 \times 8.6 - 5 = 160.12\)
- Identify the equivalent options: \(\boxed{A, C}\).
Explanation
- Evaluate the target expression
To determine the equivalent expressions, we first evaluate the core components provided in the problem description. The expression given as the focus is \(4.2 + 15 \times (8.6 - 5)\).
First, we solve the subtraction within the parentheses:
\[ 8.6 - 5 = 3.6 \]
Next, we perform the multiplication:
\[ 15 \times 3.6 = 54 \]
Finally, we add the remaining value:
\[ 4.2 + 54 = 58.2 \]
Thus, the target value is \(58.2\).
- Evaluate and compare the given options
Now, we evaluate each of the given options (A, B, C, D, E) to see which match the target value of \(58.2\):
- A. \(4.2 + 15 \times 3.6 = 4.2 + 54 = 58.2\)
- B. \(19.2 \times 3.6 = 69.12\)
- C. \(4.2 + 54 = 58.2\)
- D. \(4.2 + 15 \times 8.6 - 5 = 4.2 + 129 - 5 = 128.2\)
- E. \(19.2 \times 8.6 - 5 = 165.12 - 5 = 160.12\)
Comparing these results, both A and C evaluate to \(58.2\), which is equivalent to the target expression.
- Conclusion
Based on our evaluations, options A and C are both equivalent to the target expression \(4.2 + 15 \times (8.6 - 5)\), as they all result in \(58.2\). The final answer is A and C.
Examples
This type of algebraic evaluation is essential in daily life for tasks like budget planning or unit conversion. For example, if you are buying items for a school project, you might calculate the total cost by multiplying the number of units by their price and adding a fixed service fee. Recognizing equivalent ways to write these cost expressions helps in verifying your total and ensuring accuracy in your financial planning.