Find among the numbers such that 3/64 of it is 48.
The correct answer and explanation is:
To find the number such that 3/64 of it equals 48, we can set up an equation to solve for the unknown number. Let the unknown number be represented by xx.
The equation is: 364×x=48\frac{3}{64} \times x = 48
Step 1: Solve for xx
To isolate xx, first multiply both sides of the equation by the reciprocal of 364\frac{3}{64}, which is 643\frac{64}{3}. This will cancel out the fraction on the left-hand side: x=48×643x = 48 \times \frac{64}{3}
Step 2: Perform the multiplication
Now multiply 48 by 643\frac{64}{3}: x=48×643=30723x = \frac{48 \times 64}{3} = \frac{3072}{3}
Step 3: Simplify the fraction
Next, divide 3072 by 3: x=1024x = 1024
Thus, the number is 1024.
Verification
To verify the result, let’s check if 364\frac{3}{64} of 1024 is indeed 48: 364×1024=3×102464=307264=48\frac{3}{64} \times 1024 = \frac{3 \times 1024}{64} = \frac{3072}{64} = 48
The result is correct.
Conclusion
The number such that 3/64 of it is 48 is 1024. This problem is solved using basic algebraic principles, specifically manipulating fractions and isolating the unknown variable.