Question

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

Answer 1

Hence, the cost for 6 calculators is:

$ 133

Explanation:

Let it follows the quadratic model.

i.e let

`p(x)=ax^2+bx+c`

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:

`9a+3b+c=61-------------(1)`

and cost of 7 calculators is: $ 165

i.e.
`49a+7b+c=165--------------(2)`

and cost of 12 calculators is: $385

i.e.
`144a+12b+c=385--------------(3)`

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

`40a+4b=104`

on dividing both side by 4 we get:

`10a+b=26---------(4)`

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

`19a+b=44-------------(5)`

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

`9a=18\\\\i.e.\\\\\\a=2`

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

`b=6`

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

`c=25`

Hence, the function that models the cost is:

`p(x)=2x^2+6x+25`

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

when x=6 we have:

`p(x)=2* 6^2+6* 6+25\\\\\\i.e.\\\\\\p(x)=133`

The cost of 6 calculators is:

$ 133