Acompany produces 3 types of widgets. on a given day, the company was able to produce 9 total widgets (combining all 3 types). widget a costs $3 to produce, widget b costs #2 to produce, and widget c costs $1 to produce. the cost to produce the widgets each day is $18. the company produces one more widget b than the sum of the widgets a & c. how many of each type of widget is produced?

set up three equations with three variables. then, use a matrix to solve for the number of each type of widget.

2 widgets A, 5 widgets B and 2 widgets C

Step-by-step explanation:

Let

1.  On a given day, the company was able to produce 9 total widgets, then

2. The company produces one more Widget B than the sum of the Widgets A & C, then

3. Widget A costs $3 to produce, so x widgets A cost $3x.

Widget B costs $2 to produce, so y widgets B cost $2y.

Widget C costs $1 to produce, so z widgets C cost $z.

The cost to produce the widgets each day is $18, thus

4. We get the system of three equations:

Write an augmented matrix for this system

Therefore,

Hence

step-by-step explanation: h: (- 3, 6)

m: (1, - 2)

o: (7, 6)

r: (- 9, - 2)

midpoint of hm: (- 1, 2)

midpoint of or: (- 1, 2)

therefore, b is the midpoint of both diagonals bisect each other !

to prove the diagonals are perpendicular, show that the product of the slopes = - 1

345

step-by-step explanation: