Part a: sydney made $18.50 selling lemonade, by the cup, at her yard sale. she sold each cup for $0.50 and received a $3 tip from a neighbor. write an equation to represent this situation.
part b: daria made a profit of $21.00 selling lemonade. she sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbor, but also had to buy each plastic cup she used for $0.10 per cup. write an equation to represent this situation.
part c: explain how the equations from part a and part b differ.
answer as best as you can in sentences

part a.  

.5x+3=18.5

part b.

.65x+3=21

part c.

in the explanation.

step-by-step explanation:

part a: she made 18.50.   she sold each cup for .50 and receive a 3 dollar tip.

we don't know how many cups she sold so i'm to call this x.

.5x is how much she made just on selling cups of lemonade.

she also got a 3 dollar tip in addition so that means we have .5x+3.   we are given that this amount should be 18.5 .

this means equation part part 1 should be .5x+3=18.5 .

part b.

she made a profit of 21.   she sold .75 per cup, and receive a 3 dollar tip. she also had to buy plastic cups for .1 each.

so let x represent the number of cups.

.75x is how much she made on lemonade

3 is how much she got extra

-.1x is how much she spent on each cup x.

adding that together gives:

.75x-.1x+3 and this amount is suppose to be 21 dollars.

.75x-.1x+3=21

we could simplify the equation a bit:

.65x+3=21

part c.

part a didn't include any money loss on the cups where as part b did.   they both got an extra 3 dollars from a neighbor.   daria still got more money per cup sold even after the loss of spending 10 cents per cup.  

i dont know men

step-by-step explanation:

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.