<span>30x + 30y = 450 20x + 25y = 345
Here 345 represents the total area (in sq ft) shoveled; x repres. Melinda's rate and y represents Paul's rate. We need to solve for x and y and then subtract the smaller from the larger.
</span>30x + 30y = 450 Multiply this eqn by 2: 6<span>0x + 60y = 900
</span>20x + 25y = 345 Mult this eqn by -3: -60x -75y = -1035
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-15y = -135
y = 9
This comes to 9 square feet per minute.
Now, let's find x: 30x + 30y = 450; 30x + 270 = 450; 30x = 180; x = 6
Melinda can shovel 6 sq ft in 1 min, whereas Paul can shovel 9.
The difference is (9 - 6) sq ft / min, or 3 sq ft / min (answer)
<h2>Steps</h2>
- Standard Form Equation: f(x) = ax² + bx + c
So firstly, since (0,5) is one of our values we can plug it into the standard form equation to solve for the c variable (since 0 will cancel out the a and b variable):

Now we know that the value of c is 5. Next, plug in (-1,12) into the standard form equation and simplify (remember to also plug in 5 for the c variable):

Next, plug (2,15) into the standard form equation and simplify:

Now, with our last two simplified equations we will create a system of equations:

Now, I will be using the elimination method with this system. With the system, add up the equations together and you will get:

From here, we can solve for the a variable. With it, just divide both sides by 3:

Now that we know the value of a, plug it into either equation to solve for the b variable:

<h2>Answer</h2>
Putting all of our obtained values together, your final answer is:
