The expression to represent the total cost of manufacturing a remote is y = 3x + 2,000, where y is the manufacturing cost and x is the number of remotes.
The cost to manufacture 2000 remote controls is $8,000
Explanation:
Step 1; We need to determine the equation relating the x to the y values. y is the dependent value whereas x is the independent value i.e. the value of y depends on the value of x. It is given that each remote costs $3 to manufacture. So to make 1 remote it will cost 1 × $30 = $30, to make two remotes, it will cost 2 × $30 = $60 so to make x remotes it will cost x × $30 = 30x dollars. Assume y is the total manufacturing cost and x is the number of remotes to be manufactured.
y = 3x + 2,000.
Step 2; To calculate the cost to manufacture 2,000 remotes we calculate y when x = 2,000,
y = 3 × 2,000 + 2,000 = 6,000 + 2,000 = $8,000.
So it will cost $8,000 to manufacture 2,000 remotes.