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 a 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 is less than or equal to 10,000
4x + 3y is less than or equal to 45
Which combinations of computers, x, and tablets y, can the computer store order?
(8,4) (5,9) (10,2) (7,9)
To determine which combinations of computers and tablets the computer store can order, we need to solve the given system of inequalities.
The first inequality is: 875x + 235y ≤ 10,000.
The second inequality is: 4x + 3y ≤ 45.
To find the possible combinations of computers (x) and tablets (y), we will need to check each option and see if it satisfies both inequalities.
Option 1: (8,4)
For this option, x = 8 and y = 4.
875(8) + 235(4) = 10,120 which is greater than 10,000, so this option does not satisfy the first inequality.
4(8) + 3(4) = 44 which is less than 45, so this option satisfies the second inequality.
Option 2: (5,9)
For this option, x = 5 and y = 9.
875(5) + 235(9) = 9,275 which is less than 10,000, so this option satisfies the first inequality.
4(5) + 3(9) = 37 which is less than 45, so this option satisfies the second inequality.
Option 3: (10,2)
For this option, x = 10 and y = 2.
875(10) + 235(2) = 10,875 which is greater than 10,000, so this option does not satisfy the first inequality.
4(10) + 3(2) = 44 which is less than 45, so this option satisfies the second inequality.
Option 4: (7,9)
For this option, x = 7 and y = 9.
875(7) + 235(9) = 10,280 which is greater than 10,000, so this option does not satisfy the first inequality.
4(7) + 3(9) = 51 which is greater than 45, so this option does not satisfy the second inequality.
In conclusion, the only combination that satisfies both inequalities is (5,9). Thus, the computer store can order 5 computers and 9 tablets.