Question

Laura runs a food bank. On Monday she gave away \(\frac{1}{4}\) of her stock of flour. On Tuesday she gave away \(\frac{1}{3}\) of what was left from Monday. On Wednesday she gave away \(\frac{1}{2}\) of what was left from Tuesday. If she started with 1000 pounds of flour, how much was left by the end of Wednesday? A. 0 pounds B. 250 pounds C. 333 pounds D. 500 pounds

Short answer

250 pounds

Step-by-step solution

- Determine Flour Given Away on Monday

Calculate the amount of flour Laura gave away on Monday. Since she gave away \( \frac{1}{4} \) of her stock and she started with 1000 pounds: \( \frac{1}{4} \times 1000 = 250 \). Laura gave away 250 pounds of flour on Monday.

- Calculate Flour Remaining After Monday

Subtract the amount of flour given away on Monday from the initial stock: \( 1000 - 250 = 750 \). Laura had 750 pounds of flour remaining after Monday.

- Determine Flour Given Away on Tuesday

Calculate the amount of flour Laura gave away on Tuesday. Since she gave away \( \frac{1}{3} \) of what was left: \( \frac{1}{3} \times 750 = 250 \). Laura gave away 250 pounds of flour on Tuesday.

- Calculate Flour Remaining After Tuesday

Subtract the amount of flour given away on Tuesday from the remaining stock after Monday: \( 750 - 250 = 500 \). Laura had 500 pounds of flour remaining after Tuesday.

- Determine Flour Given Away on Wednesday

Calculate the amount of flour Laura gave away on Wednesday. Since she gave away \( \frac{1}{2} \) of what was left: \( \frac{1}{2} \times 500 = 250 \). Laura gave away 250 pounds of flour on Wednesday.

- Calculate Flour Remaining After Wednesday

Subtract the amount of flour given away on Wednesday from the remaining stock after Tuesday: \( 500 - 250 = 250 \). Laura had 250 pounds of flour remaining after Wednesday.

Key concepts

fractions

Understanding fractions is crucial in this exercise. Fractions represent parts of a whole. In this case, the stock of flour is divided into parts on different days.
On Monday, Laura gave away \(\frac{1}{4}\) of the flour. This means she gave away one part out of four equal parts of the initial amount.
Similarly, on Tuesday and Wednesday, the fractions \(\frac{1}{3}\) and \(\frac{1}{2}\) are used. It's important to keep track of the flour left after each day. Each fraction operates on the remaining amount, not the initial 1000 pounds.
To work with fractions, multiply the fraction by the amount to find the part given away. For example, \(\frac{1}{4}\) of 1000 pounds is:\[ \frac{1}{4} \times 1000 = 250 \text{ pounds} \]. This process repeats with the new remaining amounts.

word problems

Word problems often provide real-world scenarios. Breaking them down step by step can make them easier to handle.
Identify key information and operations. In this problem, Laura's actions each day and the fractions of the flour she gives away are critical.

• Monday: \( \frac{1}{4} \times 1000 \)
• Tuesday: \( \frac{1}{3} \times 750 \)
• Wednesday: \( \frac{1}{2} \times 500 \)

Paying attention to the sequence of events and how each fraction applies to the new remaining amount will help solve the problem step by step. This improves comprehension and ensures accuracy.

basic arithmetic

Basic arithmetic is used throughout this problem, including multiplication and subtraction.

• Multiplication: To find fractions of amounts, multiply the fraction by the quantity. For example, Monday's calculation: \(\frac{1}{4} \times 1000 = 250\)
• Subtraction: To find the remaining flour, subtract the given amount from the total. For example, after Monday: \( 1000 - 250 = 750 \)

Performing these operations correctly ensures you track the flour accurately each day. This repetition of operations builds confidence and proficiency in arithmetic. It's a great way to reinforce fundamental mathematical skills.

subtraction

Subtraction is a significant part of determining how much flour remains.
Each day, after calculating the given away flour, subtract that from the remaining stock.
Example for Monday's subtraction: \( 1000 - 250 = 750 \)
This step-by-step reduction continues for Tuesday and Wednesday. It ensures you accurately keep track of the stock after each day's distribution.
This methodical approach highlights the importance of subtraction in breaking down larger word problems into manageable steps.