You attend a baseball game with friends and visit the snack stand between innings. soda costs $2 a can, and a box of popcorn costs $1.50. you have $15 with you, and you wish to buy more cans of soda than boxes of popcorn. if x represents the number of cans of soda and y the number of boxes of popcorn, which graph represents the inequalities in this scenario?

let S(a)=2a be the function that calculates how many dollars you will spend if you buy x cans. (ex if a=3, so if you buy 3 cans, you will spend S(3)=2*3=6 dollars )

let P(a)=1.5a be the function that calculates how many dollars we you will spend on popcorns

you buy x soda and y popcorns, and you want x>y

we draw the line y=x, dashed, as we have a "strictly smaller than" inequality. The line y=x is the line containing (1, 1), (5, 5)... so (x, x). Any point below this line has x coordinate larger than the y coordinate, for example (5, 4.999), (5, 5) would be just on the line, and (5, 5.0001) just above the line.

So we color the region below the line y=x, with y=x dashed.

Next,  

S(x)+P(y) = the total cost of buying x soda and y popcorn = 15

2x+1.5y=15, 

1.5y=15-2x



this is the line with slope -4/3, and y intercept = 10.

for the points (x, y) on this line, the cost is exactly 15 dollars, assuming x and y are real numbers (not whole numbers, as they should)

but the problem does not say that you have to spend 15 dollars, that is you can spend les, so the region below it is also colored.

the intersection of the 2 colored regions is the last picture

last picture

 

Bis the answer! hope this