Maths Olympiad Prep

Track / Stage 4 / 281 of 340 #541 of 1964

Problem 541

AMC 12 late, AIME early
Algebra Difficulty 4.9 Find the answer

The sum of several addends is equal to 2b12 b-1. To one addend, 3b83 b-8 was added, and from the second, b7-b-7 was subtracted. How much must be subtracted from the third addend so that the sum becomes equal to zero?

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

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Official solution

4. Solution. If xx is the desired number, then

2b1+(3b8)(b7)x=0;x=6b22 b-1+(3 b-8)-(-b-7)-x=0 ; x=6 b-2.

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