Mr. Garcia had some blueberries. He sold 2 3/4 kilograms of the blueberries and packed the rest equally into 9 bags. Each bag contained 1/4 kilogram of blueberries. Find the mass o... Mr. Garcia had some blueberries. He sold 2 3/4 kilograms of the blueberries and packed the rest equally into 9 bags. Each bag contained 1/4 kilogram of blueberries. Find the mass of blueberries that Mr. Garcia had at first.
Understand the Problem
The question involves calculating the initial mass of blueberries Mr. Garcia had. He sold a specified amount and then divided the remaining blueberries equally into a certain number of bags, each with a defined weight. We need to find out the total weight before these transactions.
Answer
The mass of blueberries that Mr. Garcia had at first is $5$ kilograms.
Answer for screen readers
The mass of blueberries that Mr. Garcia had at first is $5$ kilograms.
Steps to Solve
- Identify the total amount of blueberries packed into bags
Mr. Garcia divided the remaining blueberries into 9 bags, and each bag contained $\frac{1}{4}$ kilogram of blueberries. Thus, the total mass in the bags is: $$ \text{Total in bags} = 9 \times \frac{1}{4} = \frac{9}{4} \text{ kilograms} $$
- Calculate the mass of blueberries remaining after selling
Mr. Garcia sold $2 \frac{3}{4}$ kilograms of blueberries. First, convert this mixed number to an improper fraction: $$ 2 \frac{3}{4} = \frac{11}{4} \text{ kilograms} $$
Now, let ( x ) be the initial mass of blueberries Mr. Garcia had. After selling some, the remaining mass is: $$ \text{Remaining} = x - \frac{11}{4} $$
- Set up the equation for remaining blueberries
We already calculated the mass remaining after selling, which is equal to the mass in the bags: $$ x - \frac{11}{4} = \frac{9}{4} $$
- Solve the equation for ( x )
To isolate ( x ), add $\frac{11}{4}$ to both sides: $$ x = \frac{9}{4} + \frac{11}{4} $$
Convert this to a single fraction: $$ x = \frac{20}{4} = 5 \text{ kilograms} $$
The mass of blueberries that Mr. Garcia had at first is $5$ kilograms.
More Information
Mr. Garcia started with 5 kilograms of blueberries. After selling some and packing the rest, he had a specific quantity left that allowed him to distribute the remaining blueberries evenly into bags.
Tips
- Incorrect conversion of mixed numbers: Always double-check the conversion from mixed numbers to improper fractions.
- Mistakes in setting up equations: Ensure that the setup correctly reflects the problem statement, particularly in identifying what remains after selling.
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