At a baseball game, a vender sold a combined total of 170 sodas and hot dogs. the number of hot dogs sold was 50 less than the number of sodas sold. find the number of sodas sold and the number of hot dogs sold

Let the number of sodas sold be x and the number of hotdogs sold be y. We can assemble a system of equations from the information given and solve.

x+y=170 (We know that soda + dogs is 170)

x-50=y (We know that dogs is equal to 50 less than sodas)

We can use substitution to solve this system of equations.

x+y=170

Sub in the value of y from the second equation

x+(x-50)=170

2x-50=170

2x=220

x=110

We now know the number of sodas sold was 110. Lets now plug this value into the equation to solve for y.

x+y=170

110+y=170

y=60

So, there were 60 hotdogs sold and 110 sodas sold.

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