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A game is played in which each throw of a ball lands in one of two holes: the closer hole or the farther hole. A throw landing in the closer hole scores 2 points, while a throw landing in the farther hole scores 5 points. A player's total score is equal to the sum of the scores on their throws. (d) The game is changed so that each throw scores 6 or 21 points instead of 2 or 5. Explain whether or not it is possible to have a total score of 182 points.

A game is played in which each throw of a ball lands in one of two holes: the closer hole or the farther hole. A throw landing in the closer hole scores 2 points, while a throw landing in the farther hole scores 5 points. A player's total score is equal to the sum of the scores on their throws. (d) The game is changed so that each throw scores 6 or 21 points instead of 2 or 5. Explain whether or not it is possible to have a total score of 182 points.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter6: Systems Of Linear Equations And Inequalities
Section6.1: Graphing Systems Of Equations
Problem 59PFA
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In the solution 3 (2a + 7b), is a multiple of 3, how can we know that it is multiple of 3?

A game is played in which each throw of a ball lands in one of two holes: the closer hole or the farther hole. A throw landing in the closer hole scores 2 points, while a throw landing in the farther hole scores 5 points. A player's total score is equal to the sum of the scores on their throws. (d) The game is changed so that each throw scores 6 or 21 points instead of 2 or 5. Explain whether or not it is possible to have a total score of 182 points. (d) If a throws each score 6 points and b throws each score 21 points, then 6a+216 or 3 (2a+7b) points are scored. Since a and b are non-negative integers, then 2a +7b is a non-negative integer, and so the total number of points scored, 3(2a + 7b), is a multiple of 3. Since 182 is not a multiple of 3, then it is not possible to have a total score of 182 points.
Transcribed Image Text:A game is played in which each throw of a ball lands in one of two holes: the closer hole or the farther hole. A throw landing in the closer hole scores 2 points, while a throw landing in the farther hole scores 5 points. A player's total score is equal to the sum of the scores on their throws. (d) The game is changed so that each throw scores 6 or 21 points instead of 2 or 5. Explain whether or not it is possible to have a total score of 182 points. (d) If a throws each score 6 points and b throws each score 21 points, then 6a+216 or 3 (2a+7b) points are scored. Since a and b are non-negative integers, then 2a +7b is a non-negative integer, and so the total number of points scored, 3(2a + 7b), is a multiple of 3. Since 182 is not a multiple of 3, then it is not possible to have a total score of 182 points.
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