Express the situation as a system of two equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by row-reducing the corresponding augmented matrix. State your final answer in terms of the original question. A corn and soybean commodities speculator invested $18,000 yesterday with twice as much in soybean futures as in corn futures. How much did she invest in each? X = $ invested in corn futures y = $ invested in soybean futures
Express the situation as a system of two equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by row-reducing the corresponding augmented matrix. State your final answer in terms of the original question. A corn and soybean commodities speculator invested $18,000 yesterday with twice as much in soybean futures as in corn futures. How much did she invest in each? X = $ invested in corn futures y = $ invested in soybean futures
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:**Problem Statement:**
Express the situation as a system of two equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by row-reducing the corresponding augmented matrix. State your final answer in terms of the original question.
**Scenario:**
A corn and soybean commodities speculator invested **$18,000** yesterday with twice as much in soybean futures as in corn futures. How much did she invest in each?
- \( x = \) $ \_\_\_\_ (invested in corn futures)
- \( y = \) $ \_\_\_\_ (invested in soybean futures)
**Approach:**
1. Define variables:
- Let \( x \) represent the amount invested in corn futures.
- Let \( y \) represent the amount invested in soybean futures.
2. Set up equations based on the given information:
- Total investment equation: \( x + y = 18,000 \)
- Investment relationship equation: \( y = 2x \)
3. Write these equations in augmented matrix form and apply row-reduction techniques to solve for \( x \) and \( y \).
4. Interpret the solutions in terms of the original scenario to identify how much was invested in each type of future.
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