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?
A. (10,2)
B. (7,9)
C. (8,4)
D. (5,9)

Answer 1

We can solve this system of inequalities by graphing the lines and shading the region that satisfies both inequalities.

First, let's graph the line 875x + 235y < 10,000. We can find the x-intercept and y-intercept of this line to help us graph it.

To find the x-intercept, we set y = 0 and solve for x:
875x + 235(0) = 10,000
875x = 10,000
x = 10,000/875
x = 11.43 (approximately)

To find the y-intercept, we set x = 0 and solve for y:
875(0) + 235y = 10,000
235y = 10,000
y = 10,000/235
y = 42.55 (approximately)

Now we can plot the points (11.43, 0) and (0, 42.55) on a graph and draw a line through them.

Next, let's graph the line 4x + 3y < 45. Again, we can find the x-intercept and y-intercept of this line to help us graph it.

To find the x-intercept, we set y = 0 and solve for x:
4x + 3(0) = 45
4x = 45
x = 45/4
x = 11.25

To find the y-intercept, we set x = 0 and solve for y:
4(0) + 3y = 45
3y = 45
y = 15

Now we can plot the points (11.25, 0) and (0, 15) on a graph and draw a line through them.

Finally, we shade the region that satisfies both inequalities. The shaded region will be below the line 875x + 235y < 10,000 and below the line 4x + 3y < 45.

Looking at the graph, we see that the only point that falls within the shaded region is (8, 4).

Therefore, the computer store can order 8 computers and 4 tablets, so the answer is C. (8, 4).