Question - Solving a Word Problem Involving Flour Amounts
Solution:
Let's solve the problem step by step.The problem states that Sally sold $$ 5 \frac{1}{2} $$ kg of flour and then had $$ 8 \frac{1}{4} $$ kg of flour left.To find out how much flour she had at first, we need to add the amount she sold to the amount she had left:\[ 5 \frac{1}{2} \text{ kg} + 8 \frac{1}{4} \text{ kg} \]First, we need to find a common denominator for the fractions $$ \frac{1}{2} $$ and $$ \frac{1}{4} $$. The least common denominator for 2 and 4 is 4. So we convert $$ \frac{1}{2} $$ to $$ \frac{2}{4} $$.Now the problem looks like this:\[ 5 \frac{2}{4} \text{ kg} + 8 \frac{1}{4} \text{ kg} \]Now we add the whole numbers and the fractions separately:Whole numbers:\[ 5 + 8 = 13 \]Fractions:\[ \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \]Therefore, the total amount of flour Sally had at first is:\[ 13 \frac{3}{4} \text{ kg} \]So the correct answer is:\[ (D) \quad 13 \frac{3}{4} \text{ kg} \]
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