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?

ANSWER CHOICES

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

The statement which best describes the steps to graph the solution to the inequality in x and y is the third option from the scale, because :

x nickels = 5x cents

y dimes in turn - 10y cents.

Multiply them together and now we have 5x + 10y cents.

Total amount sloud be less than $20 or 2000 cents.
`5x + 10y \ \textless \ 2000`

Answer 2

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

Explanation:

Let

x------> the number of nickels in the box

y------> the number of dimes in the box

we know that

`0.05x+0.10y < 20\$`

Multiply by
`100` both sides

`5x+10y < 2000` ------> inequality that represent the situation

The solution of the inequality is the triangular shaded area below the dashed line

see the attached figure

therefore

The statement which best describes the steps to graph the solution to the inequality in x and y is

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