Question
If only half as much milk is used each day, after how many days will more milk need to be purchased?
Ask by Clark Clark. in the United States
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
To find out after how many days more milk needs to be purchased when only half as much is used each day, set up the equation \( \frac{x}{2} \times n = x \). Solving for \( n \) gives \( n = 2 \) days.
Solution
To determine after how many days more milk will need to be purchased if only half as much milk is used each day, we can set up a simple equation based on the given information.
Let's assume that the initial amount of milk used each day is \( x \) gallons. If only half as much milk is used each day, the new amount of milk used each day will be \( \frac{x}{2} \) gallons.
The total amount of milk used after \( n \) days can be represented as:
\[ \text{Total milk used} = x \times n \]
Since only half as much milk is used each day, the total amount of milk used after \( n \) days will be:
\[ \text{Total milk used} = \frac{x}{2} \times n \]
We want to find out after how many days more milk will need to be purchased. This means that the total amount of milk used after \( n \) days will be equal to the initial amount of milk used each day, which is \( x \) gallons.
Therefore, we can set up the equation:
\[ \frac{x}{2} \times n = x \]
Solving this equation will give us the number of days after which more milk will need to be purchased.
Solve the equation by following steps:
- step0: Solve for \(n\):
\(\frac{x}{2}n=x\)
- step1: Multiply the terms:
\(\frac{xn}{2}=x\)
- step2: Cross multiply:
\(xn=2x\)
- step3: Divide both sides:
\(\frac{xn}{x}=\frac{2x}{x}\)
- step4: Divide the numbers:
\(n=2\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
When only half as much milk is consumed each day, the rate of consumption decreases significantly. For example, if you originally consume 2 liters per day, reducing that to 1 liter means your supply lasts twice as long. So, if you had a 10-liter supply, with the old consumption rate, you'd need to buy after 5 days, but with the new rate, you'd stretch that to 10 days before needing more! On the flip side, it’s important to keep track of any sudden changes in consumption. In a household where more people might start drinking milk, you could find yourself running low sooner than expected. So, consider regular reviews of your stock to avoid unexpected grocery runs!
