The company discovered that it costs $61 to produce 3 calculators, $165 to produce 7 calculators and $385 to produce 12 calculators how much does it cost for 6 calculators

Hence, the cost for 6 calculators is:

                      $ 133

Let it follows the quadratic model.

i.e let

where a,b and c are real numbers.

where p(x) denotes the cost of x calculators.

Now, it is given that:

The company discovered that it costs $61 to produce 3 calculators.

i.e. when x=3  p(x)=61

Hence, we get:

and cost of 7 calculators is: $ 165

i.e.  

and cost of 12 calculators is:  $385

i.e.  

on subtracting equation (2) from (1) we get:

on dividing both side by 4 we get:

on subtracting equation (3) from equation (2) and dividing by 5 we get:

Now on subtracting equation (4) from (5) we get:

and by putting the value of a in equation (4) we get:

and now putting the value of a and b in equation (1) we get:

             Hence, the function that models the cost is:

Now, we are asked to find the cost of 6 calculators

when x=6 we have:

           The cost of 6 calculators is:

                       $ 133

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step-by-step explanation: