Roger Maris and Babe Ruth are among the ten baseball players...

Roger Maris and Babe Ruth are among the ten baseball players with the most home runs in a major league baseball season. (IMAGE CANNOT COPY) The number of home runs by these players for the seasons shown are consecutive odd integers whose sum is $120 .$ Determine the number of homers hit by Ruth and by Maris.

Roger Maris and Babe Ruth are among the ten baseball players with the most home runs in a major league baseball season.
(IMAGE CANNOT COPY)
The number of home runs by these players for the seasons shown are consecutive odd integers whose sum is $120 .$ Determine the number of homers hit by Ruth and by Maris.

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Key Concepts

Sum of an Arithmetic Series

This concept is used to add up all the terms in an arithmetic sequence. The sum can be found by using the formula: sum = (number of terms)/2 × (first term + last term), or through alternative algebraic methods. It is a fundamental tool for tackling problems where a total of sequential terms is provided.

Translating Word Problems into Equations

This involves converting the verbal description of a problem into an algebraic equation. It requires identifying the unknowns, setting up expressions that relate them, and then using algebraic methods to solve for these unknown quantities. This skill is crucial when dealing with problems that involve sequences and sums.

Consecutive Odd Integers

These are odd numbers that follow one after the other, each differing by 2. Representing such numbers algebraically (for example, as x, x+2, x+4, etc.) is common in problems where a sequence of related values must be determined.

Arithmetic Sequence

An arithmetic sequence is a list of numbers with a constant difference between successive terms. In this context, the consecutive odd integers form an arithmetic sequence with a common difference of 2, which allows one to use sequence formulas to find terms or sums.

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