A computer store is placing an order for computers and tablets. Each computer costs $875, and each tablet costs $235. The store can spend at most $10,000 for these computers and tablets. The computer store has a limited amount of space for displaying the new computers and tablets. Each computer takes up 4 square feet of space, and each tablet takes up 3 square feet of space. The store has only 45 square feet of display space available for the new computers and tablets. The system of inequalities shown can be used to determine possible combinations of computers, x, and tablets, y, the store can order.

Question

A computer store is placing an order for computers and tablets. Each computer costs $875, and each tablet costs $235. The store can spend at most $10,000 for these computers and tablets. The computer store has a limited amount of space for displaying the new computers and tablets. Each computer takes up 4 square feet of space, and each tablet takes up 3 square feet of space. The store has only 45 square feet of display space available for the new computers and tablets. The system of inequalities shown can be used to determine possible combinations of computers, x, and tablets, y, the store can order.

875x+235y</10,000
4x+3y</45

Which combinations of computers, x, and tablets, y, can the computer store order?

Responses

(10,2)
(10,2)

(7,9)
(7,9)

(5,9)
(5,9)

(8,4)

Answer 1

To determine which combinations of computers and tablets the store can order, we need to find the solutions to the system of inequalities. We can do this by graphing the inequalities on a coordinate plane.

Plotting the first inequality, 875x + 235y <= 10,000:

We can rewrite this inequality in slope-intercept form as y <= (-875/235)x + (10,000/235), or y <= (-37/10)x + (40/235).
Plotting this line, we find that it has a negative slope and intersects the y-axis at approximately 0.17.

Now plotting the second inequality, 4x + 3y <= 45:

We can rewrite this inequality in slope-intercept form as y <= (-4/3)x + (45/3), or y <= (-4/3)x + 15.
Plotting this line, we find that it has a negative slope and intersects the y-axis at 15.

The shaded region of overlap between the two lines represents the solutions to the system of inequalities.

Examining the possible combinations listed:

(10,2): This combination falls within the shaded region and is a possible solution.
(7,9): This combination falls within the shaded region and is a possible solution.
(5,9): This combination falls within the shaded region and is a possible solution.
(8,4): This combination falls within the shaded region and is a possible solution.

Therefore, the possible combinations of computers and tablets the store can order are:
(10,2), (7,9), (5,9), and (8,4).