This is simply an issue of scale, as it would be for any recipe:
1) 2/3 cup
cleaner to 1/2
gal water would imply this:
(2/3)/(1/2) = 2/3 * 2 = 4/3, telling us that it is either 4 cup
cleaner to 3 gal
water*.
2) Now we need to scale 4 cups down to 1/2 cup, which is basically just dividing by 8 (that is, 4/8 = 1/2). That means that if our amount of cleaner is smaller by a factor of 8, then the amount of water would also be smaller by a factor of 8:
Remember, it was 4 cups
cleaner for 3 gal
water, so that's 4/8 (or 1/2) cups
cleaner to 3/8 gal
water.
Answer D.
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