Given:
• Sule's Sand:
Charge per ton = $5.00
Delivery fee = $200
• Greg's sand pit:
Charge per ton = $12.00
Delivery fee = $50
Let's find the graph which represents this situation.
For Sule's Sand, we have the equation for the total cost:
y = 5.00x + 200
For Greg's sand pit. we have the equation for the total cost:
y = 12.00x + 50
Thus, we have the system of equations:
y = 5x + 200
y = 12x + 50
Now, let's solve the system and find the solution.
Eliminate the equivalent sides and combine the equations:
5x + 200 = 12x + 50
Subtract 200 from both sides:
5x + 200 - 200 = 12x + 50 - 200
5x = 12x - 150
Subtract 12x from both sides:
5x - 12x = 12x - 12x - 150
-7x = -150
Divide both sides by -7:
[tex]\begin{gathered} \frac{-7x}{-7}=\frac{-150}{-7} \\ \\ x=21.42 \end{gathered}[/tex]
This means both total costs will be the same when the school orders 21.42 tonnes.
PLug in 21.42 for x in either equation:
[tex]\begin{gathered} y=5(21.42)+200 \\ \\ y=307.14 \end{gathered}[/tex]
Therefore, both lines will meet at the point:
(x, y) ==> (21.42, 307.14)
Since we have the equations:
y = 5x + 200
y = 12x + 50
Apply the slope-intercept form:
y = mx + b
Where b is the y-intercept.
This means the line representing the first equation will start at the point:
(0, 200)
The line representing the second equation will start at the point:
(0, 50)
Therefore, the correct graph is:
ANSWER:
