Hannah has to make 25 gallons of punch for a potluck. the punch is made of soda and fruit drink. the cost of the soda is $1.79 per gallon, and the cost of the fruit drink is $2.49 per gallon. hannah's budget requires that the punch cost $2.21 per gallon. how many gallons of soda and how many gallons of fruit drink does she need?

Hannah needs 10 gallons of soda and 15 gallons of fruit drink

Step-by-step explanation:

Let

x -----> the number of gallons of soda needed

y ----> the number of gallons of fruit drink needed

we know that

-----> equation A

-----> equation B

Solve the system by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (10,15)

see the attached figure

therefore

Hannah needs 10 gallons of soda and 15 gallons of fruit drink

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

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step-by-step explanation: