Solve the Problem $\$ 4.02$ , Before Tax $\$ 5.65$ , Before Tax

question 90

Multiple Choice

Solve the problem.
-Matt bought 3 pounds of oranges and 2 pounds of apples and paid $\$ 4.02$ , before tax. Andy bought 4 pounds of oranges and 3 pounds of apples and paid $\$ 5.65$ , before tax. Use this information to set up a matrix equation of the form $A X = B$ , which can be solved to determine the price per pound for oranges and apples. Solve this matrix equation to find the price per pound of oranges.
Use the fact that for $A = \left[ \begin{array} { l l } 3 & 2 \\ 4 & 3 \end{array} \right] , A ^ { - 1 } = \left[ \begin{array} { r r } 3 & - 2 \\ - 4 & 3 \end{array} \right]$ .

• A) \(\$ 0.72\) per pound
• B) \(\$ 0.74\) per pound
• C) \(\$ 0.79\) per pound
• D) \(\$ 0.76\) per pound

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Definitions:

Revealed Preference

A theory that assumes individuals' preferences can be determined by their purchasing habits.

Weak Axiom

A principle in consumer choice theory stating that if a consumer prefers bundle A over bundle B when both are available at the same prices, then the consumer will not purchase more of bundle B if its price rises.

Revealed Preference

An economic theory stating that the preferences of consumers can be understood by their purchasing habits.

Prices

The monetary value assigned to goods and services in a market, dictating the exchange rate at which these can be traded.