A clothing company has budgeted $58,000 for the purchase of 7 sewing machines. The 7 sewing machines are to be chosen from two models, model X and model Y. If a model X sewing machine costs $8,000 and a model Y sewing machine costs $9,000, how many model X sewing machines should the company purchase to use exactly the budgeted money?
58 = 8 x + 9 (7-x)
58 = 8 x - 9 x + 63
x = 5
To find the number of model X sewing machines the company should purchase, we need to determine the total cost of the sewing machines.
Let's assume the number of model X sewing machines to be purchased is x.
The cost of each model X sewing machine is $8,000, so the total cost of the model X sewing machines will be 8000x.
Since the total budget is $58,000, we can write the equation:
8000x + 9000(7 - x) = 58000
To solve for x, let's simplify the equation:
8000x + 63000 - 9000x = 58000
-1000x + 63000 = 58000
Now we'll isolate the x term:
-1000x = 58000 - 63000
-1000x = -5000
Dividing both sides of the equation by -1000:
x = -5000 / -1000
x = 5
Therefore, the company should purchase 5 model X sewing machines to use exactly the budgeted money of $58,000.
To solve this problem, we need to find the number of model X sewing machines the company should purchase in order to spend exactly $58,000.
Let's assume the number of model X sewing machines the company should purchase is represented by the variable "x".
The budget for the purchase of 7 sewing machines is $58,000, so we have the equation:
8000x + 9000(7 - x) = 58000
Simplifying the equation, we can expand and collect like terms:
8000x + 63000 - 9000x = 58000
-1000x + 63000 = 58000
-1000x = 58000 - 63000
-1000x = -5000
Now, divide both sides of the equation by -1000:
x = -5000 / -1000
x = 5
Therefore, the company should purchase 5 model X sewing machines in order to use exactly the budgeted $58,000.