Lincoln has dimes and y quarters. He has no more than 24 coins worth at least $3.50 combined. Solve this system of inequalities graphically and determine one possible solution

let's define:

x = number of dimes

y = number of quarters.

Then the total amount of money that he has is:

x*$0.10 + y*$0.25

Now we know that:

"He has no more than 24 coins"

Then:

x + y ≤ 24

"...worth at least $3.50 combined"

x*$0.10 + y*$0.25 ≥ $3.50

Then we have two inequalities:

x + y ≤ 24

x*$0.10 + y*$0.25 ≥ $3.50

To graph these, it is easier to write them as linear equations in the slope-intercept form.

Then we need to isolate the y-variable in both equations.

we will get:

y ≤ 24 - x

y ≥ $3.50/$0.25 - x*$0.10/$0.25

In the first equation we have:

"y is smaller or equal than the line"

Then this is graphed with a solid line, and we shade all the region below the line

For the second equation, we have the inverse case, then it will be graphed with a solid line and we need to shade all the region above the line.

The solutions for the system will be all these values that are in both shaded regions.

The graph can be seen below.

In the graph, we can see that one acceptable solution can be:

x = 5

y = 15

or

x = 6

y = 16

The only other restriction we should add is:

x ≥ 0

y ≥ 0

Because Lincoln can not have a negative number of coins, so we can only find solutions in the first quadrant.

I think everyone likes playing around with those type of things

Step-by-step explanation: