Amreeshdar instead of finding the value of 7/8th of a number, found the value of 7/18th of the number. If his answer differed from the actual answer by 770, determine the number that Amreeshdar wanted to find?
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When dealing with fractions of a number, set up an equation for the difference and solve for the unknown.
Step 1: Understanding the Concept:
Let the number be $x$. The problem provides two fractions of this number and the absolute difference between them. Step 2: Key Formula or Approach:
Equation: $|\frac{7}{8}x - \frac{7}{18}x| = 770$. Step 3: Detailed Explanation:
Since $\frac{7}{8}>\frac{7}{18}$, we write:
$\frac{7}{8}x - \frac{7}{18}x = 770$.
Take $7x$ as a common factor:
$7x (\frac{1}{8} - \frac{1}{18}) = 770$.
Divide by 7:
$x (\frac{1}{8} - \frac{1}{18}) = 110$.
The LCM of 8 and 18 is 72.
$x (\frac{9 - 4}{72}) = 110$.
$x (\frac{5}{72}) = 110$.
$5x = 110 \times 72$.
$x = 22 \times 72$.
$x = 1584$. Step 4: Final Answer:
The number is 1584.