A manufacturing company has an old machine which produces 25 components per hour. The company has recently installed a new machine which produces 35 components per hour. Yesterday, both machines were in operation for different periods of time. If 430 components were produced when the total number of hours of operation was 14 hours, determine for how many hours each machine was in operation

old machine 150, new machine 280

Step-by-step explanation:

given data:

Old machine = 25t

New machine = 35t

where t = hrs

we dont know the time for old machine so we assume it to be ( t ),

while that of the new machine is ( 14-t ) hours for new machine, and sum of 430 components.

therefore;

25t +490 - 35t = 430

-10t = -60

divide both sides by -10

t = 6 hours for the first machine.

6hrs * 25 components /hr

= 150 component parts For old machine.

for new machine

= 14 - t eq1.

where ( t = 6 ), substitute t into the equation

= 14 - 6

= 8 hours for the second machine

= 8 * 35

= 280 components parts

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be