Direction (6-10): What value should come in place of (?)?
6) 5 (2/7) of (5 × 2 + (8 × 74) × 16) = ?% of 350
A. 10/49
B. 20/49
C. 5/3136
D. 5/1568
E. 5/37
Answer (1)
To solve the equation and find the value that comes in place of the question mark (?), we start by breaking down the given mathematical expression step-by-step.
The problem given is:
5\frac{2}{7} \text{ of } (5 \times 2 + (8 \times 74) \times 16) = ?% \text{ of } 350
We will solve this step-by-step:
Simplify the Expression Inside the Parentheses:
First, calculate 5 × 2 :
5 × 2 = 10
Then, calculate 8 × 74 :
8 × 74 = 592
Multiply the result by 16: 592 × 16 = 9472
Now, add the results within the parentheses: 10 + 9472 = 9482
Calculate 5 7 2 of the Result:
Convert 5 7 2 into an improper fraction:
5 7 2 = 7 37
Multiply by 9482:
7 37 × 9482 = 37 × 1354 = 50198
Understanding the Percent Calculation:
The result 50198 equals ? % of 350. Therefore,
100 ? × 350 = 50198
Solving for ? :
Rearrange the equation to solve for ? :
? = 350 50198 × 100
Simplify:
? = 350 5019800 = 14342.2857
Based on the options provided, this calculation does not exactly match any given fraction or simplified form directly. By checking the options, it's clear there might be a potential instructional oversight or simplification aspect observed in the options.
However, if we strictly evaluate the numbers: Given typical testing strategy assumptions or answer correction, among the options provided:
None of the options exactly create a fractional percentage corresponding exactly. Hence, in an exam setting, you may re-evaluate initial computations performed or probe additional context based on options provided.
