Question

Sally has only nickels and dimes in her money box. She knows that she has less than $20 in the box. Let x represent the number of nickels in the box and y represent the number of dimes in the box. Which of the following statements best describes the steps to graph the solution to the inequality in x and y? Draw a dashed line to represent the graph of 5x + 10y = 2000, and shade the portion above the line for positive values of x and y. Draw a dashed line to represent the graph of 10x + 5y = 2000, and shade the portion above the line for positive values of x and y. Draw a dashed line to represent the graph of 5x + 10y = 2000, and shade the portion below the line for positive values of x and y. Draw a dashed line to represent the graph of 10x − 5y = 2000, and shade the portion below the line for positive values of x and y.

Answer 1

If x represent the number of nickels in the box and y represent the number of dimes in the box (note that x>0 and y>0), then the total value of x nickels is $5x and total value of y dimes is $10y. Adding these amounts of money you get that in money box was $(5x+10y).
Sally knows that she has less than $20 in the box, then 5x+10y<2000 ($20=2000 cents).

Since this inequality is strict, then you should draw the dashed line 5x+10y=2000. The line divides coordinate plane into two parts.

Pick point (0,0) and consider to which part this point belongs. Since 5·0+10·0<2000, you can conclude that (0,0) is a solution of given inequality and belongs to needed part. Hence you should take the shaded part below the line for positive values of x and y.