Maths Olympiad Prep

Track / Stage 4 / 162 of 340 #422 of 1964

Problem 422

AMC 12 late, AIME early
Algebra Difficulty 4.8 Find the answer

[ Arithmetic. Mental calculation, etc. ]
[[ Common fractions ]\quad]

After Natasha ate half of the peaches from the jar, the level of the compote decreased by one third. By what part (of the resulting level) will the level of the compote decrease if half of the remaining peaches are eaten?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Half of the peaches make up one third of the jar's volume, which is half of the remaining two thirds of the compote.

Therefore, half of this half makes up a quarter of the remaining compote in the jar.

## Answer

One quarter.

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