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.
is it b or c ?!?!?!
First of all, I would have reduced the equation to
x + 2y = 400 , so now you can mentally find the x and y intercepts as (400,0) and (0,200)
See how easy it is now to sketch the line ?
so you clearly want all the stuff below that line in the first quadrant
your answer has to be c
for b , Sally would have MORE than $20 in her bank
The correct answer is option C: "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."
To determine the correct statement, let's analyze the given information.
We know that x represents the number of nickels in the box, and y represents the number of dimes. We also know that Sally has less than $20 in the box.
To find an inequality that represents this situation, we need to consider the values of nickels and dimes and their respective values in cents. Since there are 5 cents in a nickel, and 10 cents in a dime, we can express the total value (in cents) as:
5x + 10y < 2000
Now, let's analyze the options given:
a) Draws 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.
It represents an equation (not an inequality), and it doesn't match the given inequality.
b) Draws 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.
This option represents an equation that doesn't match the given inequality. Furthermore, shading above the line would indicate values of x and y greater than the solution, which contradicts the fact that Sally has less than $20.
c) Draws 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.
This is the correct option. It represents the inequality mentioned above since the dashed line indicates the equality, and shading below the line indicates the values satisfying the inequality (i.e., less than $20).
d) Draws 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.
This option represents an equation that doesn't match the given inequality.
Therefore, the correct statement is option c) "Draws 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."