standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
we can do away with the denominators by simply multiplying both sides by the LCD of all fractions, in this case that'd be 4.
We need 56 pints of the 55 % <em>pure fruit</em> juice and 84 pints of the 80 % <em>pure fruit</em> juice to prepare 140 pints of 70 % <em>pure fruit</em> juice.
<h3>How to use weighted averages to find the correct juice concentration</h3>
In this problem we have to use two kinds of juice with different concentrations. To get a certain concentration, we must adjust quantities of each kind and <em>weighted</em> averages offers a method that is easy to apply:
70 · 140 = 55 · x + 80 · (140 - x)
70 · 140 = 80 · 140 - 25 · x
25 · x = 10 · 140
x = 56
We need 56 pints of the 55 % <em>pure fruit</em> juice and 84 pints of the 80 % <em>pure fruit</em> juice to prepare 140 pints of 70 % <em>pure fruit</em> juice.
To learn more on weighted averages: brainly.com/question/28042295
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The process of elimination is where you set the two equations up like a subtraction problem and cancel out one of the variables. We first need to manipulate the equations so that we can get one of the variables to be the same in both equations.
One way to do so would be multiplying the first equation by 3 and the second equation by 8. That gives us the following:
24x - 21y = 15
24x - 40y = 72
Now multiply one of them by -1 so that we can cancel the x out
24x - 21y = 15
-24x + 40y = -72
_______________
0x + 19y = -57
y = -57/19
y=-3
So 30% of the 50 t-shirts need to be small.
You can just multiply the two together, to get 15 shirts that need to be small.
Long way: 30% = 3/10
1/10 of 50 is 5
1/10 * 3 = 3/10
5 * 3 = 3/10
15 = 3/10
Since you are subtracting a negative you would add them together equaling -10
