Question

PLEASE HELP MEEE

Lisa has only nickels and dimes in her money box. She knows that she has less than $15 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 = 1500 and shade the portion below the line for positive values of x and y.

Draw a dashed line to represent the graph of 5x + 10y = 1500 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 = 1500 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 = 1500 and shade the portion below the line for positive values of x and y.

Answer 1

The answer is A. Each nickel is worth 5 cents and each dime is worth 10 cents so 5x +10y is less then or equal to 1500

Answer 2

Draw a dashed line to represent the graph of 5x + 10y = 1500 and shade the portion below the line for positive values of x and y.

Explanation:

Here, x represent the number of nickels in the box and y represent the number of dimes in the box.

We know that,

1 nickel = 0.05 dollar,

So, the cost of each nickel is $ 0.05,

Also, 1 dime = 0.10 dollar

So, the cost of each dime is $ 0.10,

Thus, the total cost of x nickel and y dimes = (0.05x + 0.10y) dollars,

According to the question,

Total cost < $ 15,

⇒ 0.05x + 0.10y < 15

⇒ 5x + 10y < 1500 ( Multiplicative property of inequality ),

Which is the required inequality that represents the given situation, where x ≥ 0 and y ≥ 0 ( Number can not be negative )

Graphing :

Since, the related equation of the above inequality is, 5x + 10y = 1500

And, 5(0) + 10(0) < 1500 ( True )

So, the shaded portion would be below the line,

Also, '<' shows the dashed line,

Hence, first option is correct.