Aya poured $6$ ounces of coffee into a cup and a whole number of ounces of cream into a second cup. She then poured $4$ ounces of the coffee from the first cup into the second and, after stirring thoroughly, poured half the liquid in the second cup back into the first. If more than half of the liquid in the first cup was then cream, what was the smallest possible number of ounces of cream that was originally in the second cup?

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Comments

MahnoorSep 30

This one took me a while but the key is tracking what happens after the first transfer. Took me a second to realize the second cup's concentration changes before she pours half back.

Raihana5d ago

Same here, the double transfer was the tricky part. Once I set it up with variables it clicked.

Arpan3h ago

I kept wanting to just average the two cups, which is totally wrong here.

GurpreetSep 20

Wait, can someone explain why we can't just say more than half of the final first cup is cream? The first cup already had 2 oz coffee left, so the amount poured back has to be mostly cream...

HarshalaSep 22

Careful, the liquid poured back is a mix, not pure cream. That's where the algebra comes in.

ShreyaSep 27

Right, the second cup is homogeneous after stirring, so whatever comes back has the same ratio.

WilsonMay 13

Getting D, but honestly this felt more like a 700+ for me. The inequality setup at the end was annoying to keep straight.

YashikaMay 18

Agreed, the plugging-in of choices near the end made it faster for me.

BebasSep 24

Thanks for posting this, mixture problems always get me. Setting c as the original cream and building the fraction step by step helped.

What this question tests

What it tests

Your ability to reason about weighted averages and the composition of mixtures.

Common trap

Averaging the percentages of two solutions without weighting by their volumes.