I don't know what the "six-step method" is supposed to be, so I'll just demonstrate the typical method for this problem.
Let <em>x</em> be the amount (in gal) of the 50% antifreeze solution that is required. The new solution will then have a total volume of (<em>x</em> + 60) gal.
Each gal of the 50% solution used contributes 0.5 gal of antifreeze. Similarly, each gal of the 30% solution contributes 0.3 gal of antifreeze. So the new solution will contain (0.5 <em>x</em> + 0.3 * 60) gal = (0.5 <em>x</em> + 18) gal of antifreeze.
We want the concentration of antifreeze to be 40% in the new solution, so we need to have
(0.5 <em>x</em> + 18) / (<em>x</em> + 60) = 0.4
Solve for <em>x</em> :
0.5 <em>x</em> + 18 = 0.4 (<em>x</em> + 60)
0.5 <em>x</em> + 18 = 0.4 <em>x</em> + 24
0.5 <em>x</em> - 0.4 <em>x</em> = 24 - 18
0.1 <em>x</em> = 6
<em>x</em> = 6/0.1 = 60 gal
One hundred eighty-seven and twenty-three thousandths
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Answer:
Shannon run 1.5 km more on Friday than on Saturday.
Step-by-step explanation:
From the given table
- Distance run on Friday = 4/2 = 2 km
- Distance run on Saturday = 1/2 = 0.5 km
- In order to run how many more kilometers Shannon run on Friday than on Saturday, we need to subtract the distance run on Saturday from the distance run on Friday.
i.e.
Friday run - Saturday run = 2 - 0.5
= 1.5 km
Thus, Shannon run 1.5 km more on Friday than on Saturday.
The solutions for the quadratic equation are given as follows:
x = -1, x = 7/5
<h3>What is a quadratic function?</h3>
A quadratic function is given according to the following rule:
y = ax^2 + bx + c
The solutions are:
In which:
For this problem, the equation is:
5x² - 2x - 7 = 0.
Hence the coefficients are a = 5, b = -2 and c = -7, and then the solutions are found as follows:
The solutions are:
x = -1, x = 7/5
More can be learned about quadratic equations at brainly.com/question/24737967
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