Determine if segment XY is tangent to circle Z.
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X = gallons of the 7% butterfat milk
y = gallons of the 2% butterfat milk
now, we'll be adding "x" gallons of the 7% one, but we know that, is really "x" gallons, but only 7% of it is butterfat, the rest is water and other subtances.
so, in "x" gallons, how many gallons is butterfat only anyway? namely, what is 7% of "x"? well, (7/100) * x, or 0.07x.
likewise, how many gallons of butterfat are in the 2% one? well, (2/100) * "y" or 0.02y.
we know that, whatever "x" and "y" add up to 275 gallons, thus x + y = 275.
we also know that, the butterfat amounts add up to the same butterfat in the 275 gallons, thus
how much will it be of the 2% milk? well, y = 275 - x.
y = gallons of the 2% butterfat milk
now, we'll be adding "x" gallons of the 7% one, but we know that, is really "x" gallons, but only 7% of it is butterfat, the rest is water and other subtances.
so, in "x" gallons, how many gallons is butterfat only anyway? namely, what is 7% of "x"? well, (7/100) * x, or 0.07x.
likewise, how many gallons of butterfat are in the 2% one? well, (2/100) * "y" or 0.02y.
we know that, whatever "x" and "y" add up to 275 gallons, thus x + y = 275.
we also know that, the butterfat amounts add up to the same butterfat in the 275 gallons, thus
how much will it be of the 2% milk? well, y = 275 - x.