Maths Olympiad Prep

Track / Stage 5 / 49 of 400 #649 of 1964

Problem 649

AIME late
Algebra Difficulty 5.1 Find the answer

2.1. A metal weight has a mass of 20 kg and is an alloy of four metals. The first metal in this alloy is one and a half times more than the second, the mass of the second metal is to the mass of the third as 3:43: 4, and the mass of the third to the mass of the fourth - as 5:65: 6. Determine the mass of the fourth metal. Give the answer in kilograms, rounding to hundredths if necessary.

A number or a short expression. Spacing and $ signs are ignored.

Official solution

2.1. A metal weight has a mass of 20 kg and is an alloy of four metals. The first metal in this alloy is one and a half times more than the second, the mass of the second metal is to the mass of the third as 3:43: 4, and the mass of the third to the mass of the fourth - as 5:65: 6. Determine the mass of the fourth metal. Give the answer in kilograms, rounding to hundredths if necessary.

{5.89}\{5.89\}

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