Question

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

Convert dollars into cents to get a constant unit for the variables listed:


`\text{100 cents in a dollar}`

`15 * 100 = 1500`

We now have the following values:


`\text{Nickel = 5 cents}`

`\text{Dime = 10 cents}`

`\text{Amount in box = 1500 cents}`

Because there are multiple nickels and dimes in the box, give them variables:


`\text{Amount of nickels = x}`

`\text{Total value of nickels = 5x}`


`\text{Amount of dimes = y}`

`\text{Total value of dimes = 10y}`

Since we are determining the total value of both nickels and dimes in the box, we will add them together to total the value of the box:


`5x + 10y = 1500`

The question states that Lisa has less than $15, or 1500 in the box. The inequality will now read as follows:


`5x + 10y \ \textless \ 1500`

When graphed, the shaded part of the graph will be below the line, as it represents all values of x and y that would result in an output under 1500.

The answer is "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.".