Sugar cost \(37\dfrac{1}{2}\) per kg. Find the cost of \(8\dfrac{3}{4}\)kg of sugar

Step 1: Converting the given statement into mathematical expression.

If 1 kg of sugar costs Rs.\(37\dfrac{1}{2}\), then \(8\dfrac{3}{4}\)kg of sugar will cost:
Cost =\( 8\dfrac{3}{4}\times37\dfrac{1}{2}\)

Step 2: Convert the mixed fractions into improper fractions and find the total cost
We have
Cost = \(8\dfrac{3}{4}\times37\dfrac{1}{2} \)

\(Mixed fraction=\dfrac{integral part\times denominator+Numerator}{Denominator}\)
We will use the above formula to convert the mixed fracation into improper fraction

=\(\dfrac{8\times 4+3}{4} +\dfrac{37\times 2+1}{2}\)

=\(\dfrac{ 32+2}{4} +\dfrac{ 74+1}{2}\)

=\(\dfrac{ 35}{4} \times \dfrac{ 75}{2}\)

=\(\dfrac{2625}{8}=328\dfrac{1}{8}\)Rs

Hence, the cost of \(8\dfrac{3}{4}\)kg of sugar is Rs.\(328\dfrac{1}{8}\)