Ms. Vasquez's daughter lives 1,650 miles away. Ms. Vasquez won a gift card for 100 gallons of gas. If her car can travel 35 miles on each gallon, can she travel roundtrip to see her daughter on free gas? Explain how you know.

yes, since it takes 48 gallons of gas to go one direction to go back it is 96

Step-by-step explanation:

Yes

Step-by-step explanation:

If her daughter lives 1,650 miles away, and her gift card is for q00 miles of gas, and her car can travel 35 miles on each gallon, it would take about 47 gallons to make the 1,650 mile trip to her daughter. Leaving 53 gallons on her car.

To make the 1,650 mile trip back to her own home, it would take another 47 gallons. Since she still has 53 gallons left from her trip there, she will be able to make the trip back with still 6 gallons in her tank.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

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.