A hair product company sells three types of hair products for $30,$20 and $10 per unit.In one year,the total revenue for the three products was $820,000 which corresponded to the sale of 42,000 units.The company sold half as many units of the $30 products as units of the $20 product.Use Cramer's Rule to solve a system of linear equations to find how many units of each product were sold.
A)10,000 units at $30,20,000 units at $20,12,000 units at $10.
B)10,000 units at $30,20,000 units at $20,18,000 units at $10.
C)10,000 units at $30,20,000 units at $20,20,000 units at $10.
D)10,000 units at $30,20,000 units at $20,14,000 units at $10.
E)10,000 units at $30,20,000 units at $20,16,000 units at $10.

Question

A hair product company sells three types of hair products for $30,$20 and $10 per unit.In one year,the total revenue for the three products was $820,000 which corresponded to the sale of 42,000 units.The company sold half as many units of the $30 products as units of the $20 product.Use Cramer's Rule to solve a system of linear equations to find how many units of each product were sold. ​
A)10,000 units at $30,20,000 units at $20,12,000 units at $10.
B)10,000 units at $30,20,000 units at $20,18,000 units at $10.
C)10,000 units at $30,20,000 units at $20,20,000 units at $10.
D)10,000 units at $30,20,000 units at $20,14,000 units at $10.
E)10,000 units at $30,20,000 units at $20,16,000 units at $10.

Quizplus · Accepted Answer

The system of equations based on the given information is: $30x + 20y + 10z = 820,000$, $x + y + z = 42,000$, and $x = \frac{1}{2}y$. Solving this system using Cramer's Rule or substitution yields $x = 10,000$, $y = 20,000$, and $z = 12,000$, which corresponds to choice A.

A Hair Product Company Sells Three Types of Hair Products