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 $2 b-1$ . To one addend, $3 b-8$ was added, and from the second, $-b-7$ was subtracted. How much must be subtracted from the third addend so that the sum becomes equal to zero?

Your answer

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

Official solution

4. Solution. If $x$ is the desired number, then

$2 b-1+(3 b-8)-(-b-7)-x=0 ; x=6 b-2$ .

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