Travis has xx nickels and yy dimes. He has no more than 20 coins worth a minimum of $1.40 combined. Solve this system of inequalities graphically and determine one possible solution.

Question

Travis has xx nickels and yy dimes. He has no more than 20 coins worth a minimum of $1.40 combined. Solve this system of inequalities graphically and determine one possible solution.

Answer 1

1 - the total number of coins is no more than 20 so --> x + y ≤ 20 (solve for y)

2 - the total value of the coins is at least $1.40 so --> .05x + .10y ≥ 1.40 (solve for y)

Graph each using y=mx+b so you can see the intercepts because you just solved for y above.

The shade in the graph using the ≤ or ≥ accordingly

Answer 2

We can write the system of inequalities as follows:

x + y <= 20 ----> Number of Nickels (x) and number of Dimes (y) is no greater than (<=) 20

0.05x + 0.1y => 1.40 -----> Value of a nickel (0.05) times number nickels (x) and value of dime (0.1) time number of dimes (y) is greater than or equal to (=>) 1.40

You would then graph these two equations and determine on possible solution from that graph.

Answer 3

Write an equation about the number of coins. Then write an equation about their VALUE.

xx + yy ≤ 20

5xx + 10yy ≥ 140

Graph the inequalities using shading. Choose a point in the shaded area for your answer.

One possibility is 5 nickels and 12 dimes.