Answer:
Card 7
The hourly rate of change/slope is $75 per hour.
Card 8
Frastastic is charging $0.48 per ounce.
Step-by-step explanation:
Card 7
Lets take the set up fee as "$[tex]s[/tex]" and,
Hourly rate as $[tex]x[/tex]per hour.
Now we can write equations for 3 hour event and 5 hour event.
[tex]s+3x=275[/tex] <------- (1)
[tex]s+5x=425[/tex] <------- (2)
Now we need to solve the simultaneous equations to find [tex]s[/tex] and [tex]x[/tex].
Subtract (1) from (2)
⇒[tex]s+5x-(s+3x)=425-275[/tex]
[tex]s+5x-s-3x=150[/tex]
[tex]2x=150[/tex]
[tex]x=75[/tex]
So the hourly rate of change/slope is $75 per hour.
Therefore, Raymond is right.
Card 8
You can take Amount (oz) as x values and Cost as y values and plot a graph.
Then the Slope of the graph will give you the rate Frastastic is charging per yogurt.
Slope of a linear graph is given by the following equation;
Slope(m)=[tex]\frac{y_{1}-{y_{2}}} {x_{1}-x_{2} }[/tex]
Slope(m)=[tex]\frac{6.72-2.4}{14-5}[/tex]
Slope(m)=[tex]\frac{4.32}{9}[/tex]
Slope(m)=[tex]0.48[/tex]
Therefore, Frastastic is charging $0.48 per ounce.
This is less than $0.50 per ounce charged by Fromazing. Therefore, Sterling is right.
