Convert dollars into cents to get a constant unit for the variables listed:
[tex]\text{100 cents in a dollar} [/tex]
[tex]15 \times 100 = 1500[/tex]
We now have the following values:
[tex]\text{Nickel = 5 cents}[/tex]
[tex]\text{Dime = 10 cents}[/tex]
[tex]\text{Amount in box = 1500 cents}[/tex]
Because there are multiple nickels and dimes in the box, give them variables:
[tex]\text{Amount of nickels = x} [/tex]
[tex]\text{Total value of nickels = 5x}[/tex]
[tex]\text{Amount of dimes = y} [/tex]
[tex]\text{Total value of dimes = 10y}[/tex]
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:
[tex]5x + 10y = 1500[/tex]
The question states that Lisa has less than $15, or 1500 in the box. The inequality will now read as follows:
[tex]5x + 10y \ \textless \ 1500[/tex]
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.".
