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Systems of Linear Equations

Problem 1. Investments. William opened two investment accounts for his grandson's college fund. The first year, these investments, which totaled $18,000, yielded $831 in simple interest. Part of the money was invested at 5.5% and the rest at 4%. How much was invested at each rate?

Problem 2.
"Arctic Antifreeze" is 18% alcohol and "Frost No-More" is 10% alcohol. How many liters of Arctic Antifreeze should be mixed with 7.5 L of Frost No-More in order to get a mixture that is 15% alcohol?

How does the author determine what the first equation should be?
What about the second equation?
How are these examples similar?
How are they different?

Solution Preview

Please see the attachment for solution. If you need any further clarification please ask me. Thank you.

How does the author determine what the first equation should be?

The first equation is based on the total number of objects. It is usually in the form:
x + y = m, where x and y are variables representing the objects in the problem and m is the total number of objects, combined.

What about the second equation?

The second equation comes from the values of each object, the interest rates of the loans, or other percentages given in the problem (you can think of all of these as "rates"). The sum of the price of each object times the number of objects for each object should equal the total price for the two combined.

How are ...

Solution Summary

The solution contains some basic mathematics problems using the system of linear equations.