Question

sebastian has x nickles and y pennies. he has at least 20 coins worth at most $0.65 combined. sliver this system of inequalities graphically and determine one possible solution

Answer 1

we'll assign variables and set up the inequalities:

Let x be the number of nickels (worth 5 cents each).

Let y be the number of pennies (worth 1 cent each).

The inequalities can be written as follows:

1. x + y ≥ 20 (There are at least 20 coins.)

2. 5x + y ≤ 65 (The combined value of the coins is at most $0.65.)

To graph this system, we'll plot the two inequalities on a coordinate plane:

1. Graph the line x + y = 20:

- Plot the points (0, 20) and (20, 0) and draw a line passing through them.

2. Graph the line 5x + y = 65:

- Plot the points (0, 65) and (13, 0) and draw a line passing through them.

The region where the shaded areas of the two lines overlap represents the possible solutions. It represents the values of x and y that satisfy both inequalities.

Here is a visual representation of the graph:

```

|

65 | x + y = 20

| /

| /

| /

| /

| /

0 +-------------------------

0 10 20 30 40 50

x

```

(I am so artistic)

One possible solution that lies in the shaded region is x = 10 (nickels) and y = 10 (pennies). This satisfies both inequalities: x + y = 20 and 5x + y = 65.

Answer 2

Let's define the variables:

x = number of nickels

y = number of pennies

According to the problem, we have the following conditions:

x and y are non-negative integers.

The total number of coins is at least 20: x + y ≥ 20

The combined value of the coins is at most $0.65: 0.05x + 0.01y ≤ 0.65

To graphically represent this system of inequalities, we can plot it on a coordinate plane with x on the horizontal axis and y on the vertical axis. Let's start by graphing the individual equations and then shading the feasible region that satisfies all the conditions.

Graph:

x + y ≥ 20: This is a line passing through the points (20, 0) and (0, 20), including all the points above and on the line.

0.05x + 0.01y ≤ 0.65: Let's rewrite it as 5x + y ≤ 65 by multiplying both sides by 100. This is a line passing through the points (0, 65) and (13, 0), including all the points below and on the line.

Feasible Region:

To find the feasible region, we need to shade the area that satisfies both inequalities. It will be the area where the shaded regions of the two lines overlap.

By graphing the inequalities, we find that the feasible region is a triangle with vertices at (0, 20), (13, 7), and (13, 0).

One possible solution within this feasible region is x = 13 nickels and y = 7 pennies, as it satisfies all the given conditions.