Algebra Question Context

Question

Sarah has x nickels and y dimes. She has a maximum of 18 coins worth no less than $1.20 combined. Solve this system of inequalities graphically and determine one possible solution. Come up with two inequalities

Answer 1

x + y <= 18

5x+10y>=120 amount in pennies

solves by eq2 - 5*eq --> 5x+10y - 5(x+y) = 120 - 5*18

5x + 10y -5x-5y = 120 - 90

5y = 30

y=6

the intersection of lines is (x=12, y=6)

12 nickels 6 dimes is the starting point

You can graph at www dot desmos dot com

Here's the table.

nickels dimes count $$$$$

0 12 12 120

0 13 13 130

0 14 14 140

0 15 15 150

0 16 16 160

0 17 17 170

0 18 18 180

1 17 18 175

1 16 17 165

1 15 16 155

1 14 15 145

1 13 14 135

1 12 13 125

2 16 18 170

2 15 17 160

2 14 16 150

2 13 15 140

2 12 14 130

2 11 13 120

3 15 18 165

3 14 17 155

3 13 16 145

3 12 15 135

3 11 14 125

4 14 18 160

4 13 17 150

4 12 16 140

4 11 15 130

4 10 14 120

5 13 18 155

5 12 17 145

5 11 16 135

5 10 15 125

6 12 18 150

6 11 17 140

6 10 16 130

6 9 15 120

7 11 18 145

7 10 17 135

7 9 16 125

8 10 18 140

8 9 17 130

8 8 16 120

9 9 18 135

9 8 17 125

10 8 18 130

10 7 17 120

11 7 18 125