Large reusable bottles cost $4 more than small ones. eight large bottles cost $24 less than 12 small ones. how much does one small bottle cost?

A small bottle costs $14.

To solve the problem, the equation would be this:

 

Let s represent a small bottle. Since one large bottle is $4 more than a small one, you would write out (4+s). Then, multiply it by 8 to find one side of the equation, and get 8(4+s). To write out the right side of the equation, you would write out 12s to represent 12 small bottles, and subtract 24 from that to represent that 8 large bottles is $24 less than 12 small ones. 

Then, proceed to solve the equation to get the answer of s=14. Because a small bottle is $14, you can check your work by substituting the 14 in replace of s. 

and y≤ -x +4 .

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

y≤ -x +4 .

Where is the diagram