Track / Stage 5 / 89 of 400 #689 of 1964

Problem 689

AIME late

Algebra Difficulty 5.1 Find the answer

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 $3: 4$ , and the mass of the third to the mass of the fourth - as $5: 6$ . Determine the mass of the fourth metal. Give the answer in kilograms, rounding to hundredths if necessary.

Your answer

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

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 $3: 4$ , and the mass of the third to the mass of the fourth - as $5: 6$ . Determine the mass of the fourth metal. Give the answer in kilograms, rounding to hundredths if necessary.

$\{5.89\}$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.