Question

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league. What does the solution of the system represent in this context?

StartLayout Enlarged Left-Brace 1st Row y = 35 x 2nd Row y = negative 0.05 (x minus 400) squared + 9,942 EndLayout
the number of sweatshirts that generate the maximum income
the number of sweatshirts that generate the minimum cost
the number of sweatshirts for which the difference between cost and income is greatest.
the number of sweatshirts for which cost and income are equal

Answer 1

The solution of the system represents "the number of sweatshirts for which cost and income are equal"  Option D

This is further explained below.

What does the solution of the system represent in this context?

Let y_1 represent the revenue from selling " x" sweatshirts and y_2 represent the cost of producing " x " sweatshirts, solving the system:

$y_1=35 x\\\\y_2=-0.05(x-400)^2+9.492\\\\y_1=y_2\\\\35 x=-0.05(x-400)^2+9,492\\\\-0.05(x-400)^2-35 x+9,492=0$

The answer to the equation in the previous paragraph is the number of sweatshirts for which the cost of manufacturing y 2 is equivalent to the income obtained from sales.

In conclusion, the solution represents the number of sweatshirts for which cost and income are equal.

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