In a game, players have 60 seconds to toss rings into boxes. Rings that land in green boxes, g, earn 5 points
Rings that land in blue boxes, b, earn 10 points
Players must earn at least 50 points to win
Which inequality models the combination of tosses needed to win?

g*5 + b*10 ≥ 50.

Step-by-step explanation:

Let's define g = number of rings that land in green boxes.

and b = number of rings that land in blue boxes.

For each ring in the green box you earn 5 points, then if there are g rings in the green box, you have g*5 points.

And for the blue is similar, if there are b rings in the blue box, you will have b*10 points.

Then the total number of points that you will get is:

T = g*5 + b*10.

And the minimum that you need to win is 50 points, the inequality will be:

T ≥ 50

or

g*5 + b*10 ≥ 50.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3