a company makes couches, tables, and nightstands. each item uses units of wood, fabric, and stuffing.\n…

a company makes couches, tables, and nightstands. each item uses units of wood, fabric, and stuffing.\n. couches use 50 units of wood, 40 units of fabric, and 45 units of stuffing.\n. tables use 30 units of wood, 15 units of fabric, and 10 units of stuffing.\n. nightstands use 5 units of wood, 5 units of fabric, and 5 units of stuffing.\n\nthere are 1,100 units of wood, 760 units of fabric, and 730 units of stuffing available to make the items.\n\nwrite the three equations needed to find the largest number of x couches, y tables, and z nightstands that can be made

a company makes couches, tables, and nightstands. each item uses units of wood, fabric, and stuffing.\n. couches use 50 units of wood, 40 units of fabric, and 45 units of stuffing.\n. tables use 30 units of wood, 15 units of fabric, and 10 units of stuffing.\n. nightstands use 5 units of wood, 5 units of fabric, and 5 units of stuffing.\n\nthere are 1,100 units of wood, 760 units of fabric, and 730 units of stuffing available to make the items.\n\nwrite the three equations needed to find the largest number of x couches, y tables, and z nightstands that can be made

Answer

Explanation:

Step1: Set up wood - usage equation

The wood used for couches is 50x units, for tables is 30y units and for nightstands is 5z units. The total available wood is 1100 units. So the equation is $50x + 30y+5z=1100$.

Step2: Set up fabric - usage equation

The fabric used for couches is 40x units, for tables is 15y units and for nightstands is 5z units. The total available fabric is 760 units. So the equation is $40x + 15y+5z=760$.

Step3: Set up stuffing - usage equation

The stuffing used for couches is 45x units, for tables is 10y units and for nightstands is 5z units. The total available stuffing is 730 units. So the equation is $45x + 10y+5z=730$.

Answer:

$50x + 30y+5z=1100$ $40x + 15y+5z=760$ $45x + 10y+5z=730$