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Algebra
Pregunta

A company is running a price-test on one of its pr...

A company is running a price-test on one of its products in two separate locations. At one of the locations, the product was priced at \( \$ 120 \) . At the other location the product was priced at \( \$ 83 \) . During the price-test, total of \( 3151 \) products were sold and total revenue from sales was \( \$ 285,139 \) . How many products were sold in each location? 

Answer

\(\left[ \begin{array} { c } { x + y = 3151 } \\ { 120 x + 83 y = 285139 } \end{array} \right]\)

Isolate \( x \) for \( x + y = 3151 : x = 3151 - y \) 

Substitute \( x = 3151 - y \) 

\( [ 120 ( 3151 - y ) + 83 y = 285139 ]\) 

Simplify 

\( [ 378120 - 37 y = 285139 ] \) 

Isolate \( y \) for \( 378120 - 37 y = 285139 : y = 2513 \) 

For \( x = 3151 - y \) 

Substitute \( y = 2513 \) 

\( x = 3151 - 2513 \) 

Simplify 

\( x = 638 \) 

The solutions to the system of equations are: 

\( x = 638 , y = 2513\) 

Solución
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