Chapter 6.1, Problem 5STP

For Exercises 1-4, choose the correct letter.

A farmer feeds his cows 200 pounds of feed each day and has 700 pounds of feed in his barn. Another farmer feeds his cows 350 pounds of feed each day and has 1000 pounds of feed in his barn.

a. In how many days will the two farmers have the same amount of feed left?

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b. Does your answer make scans? Explain.

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c. How would your answer change if both farmers got an additional 1000 pounds of feed?

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To determine

To calculate. In how many days will the two farmers have the same amount of feed left?

Answer to Problem 5STP

300 pounds.

Explanation of Solution

Given:

A farmer feeds 200 pounds each day and has 700 pounds of his barn. Another farmer feeds 350 pounds each day and has 1000 pounds of feed in his barn.

Calculation:

As first farmer feeds 200 pounds each day out of 700 pounds, so the amount of feed available is

After one day = Total feed $-$ feed consumed in 1 day

  $\begin{array}{l}=700-200\\ =500\end{array}$

After two days = Total feed $-2*$ feed consumed in 1 day

  $\begin{array}{l}=700-2*200\\ =700-400\\ =300\end{array}$

Another farmer feeds 350 pounds each day out of 1000 pounds, so the amount of feed available is

After one day = Total feed $-$ feed consumed in 1 day

  $\begin{array}{l}=1000-350\\ =650\end{array}$

After two days = Total feed $-2*$ feed consumed in 1 day

  $\begin{array}{l}=1000-2*350\\ =1000-700\\ =300\end{array}$

So after two days both farmers have same amount of feed left in their barns.

Conclusion:

In two days both farmers have same amount of feed left in their barns i.e. 300 pounds.

To determine

To explain: A farmer feeds his cows 200 pounds of feed each day and has 700 pounds of his barn. Another farmer feeds his cows 350 pounds of feed each day and has 1000 pounds of feed in his barn. Does your answer make sense? Explain

Explanation of Solution

Given:

A farmer feeds 200 pounds each day and has 700 pounds of his barn. Another farmer feeds 350 pounds each day and has 1000 pounds of feed in his barn.

Reason:

As calculated in above that after two days both farmers have same amount of feed left in their barns i.e. 300 pounds.

Hence the answer make sense.

To determine

To calculate: A farmer feeds his cows 200 pounds of feed each day and has 700 pounds of his barn. Another farmer feeds his cows 350 pounds of feed each day and has 1000 pounds of feed in his barn. How would your answer change if both of the farmer got an additional 1000 pounds of feed?

Answer to Problem 5STP

theoretically there is no change in answer, but graphically it is 1000 units higher and will intersect at $x=2$ .

Explanation of Solution

Given:

both of the farmer got an additional 1000 pounds of feed.

Calculation:

As first farmer feeds 200 pounds each day out of 1700 pounds, so the amount of feed available is

After one day = Total feed $-$ feed consumed in 1 day

  $\begin{array}{l}=1700-200\\ =1500\end{array}$

After two days = Total feed $-2*$ feed consumed in 1 day

  $\begin{array}{l}=1700-2*200\\ =1700-400\\ =1300\end{array}$

Another farmer feeds 350 pounds each day out of 2000 pounds, so the amount of feed available is

After one day = Total feed $-$ feed consumed in 1 day

  $\begin{array}{l}=2000-350\\ =1650\end{array}$

After two days = Total feed $-2*$ feed consumed in 1 day

  $\begin{array}{l}=2000-2*350\\ =2000-700\\ =1300\end{array}$

So after two days both farmers have same amount of feed left in their barns.

Conclusion:

So theoretically there is no change in answer, but graphically it is 1000 units higher and will intersect at $x=2$ .