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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. (c) Tia had t throws that each scored 2 points and f throws that each scored 5 points. If Tia's total score was 37 points, determine all possible ordered pairs (t, f).

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. (c) Tia had t throws that each scored 2 points and f throws that each scored 5 points. If Tia's total score was 37 points, determine all possible ordered pairs (t, f).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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1. 4·3······2·······1· · · · · · · 0······1· · · · · · ·2······3· · · · · · 4 · · · · · · · 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. (c) Tia had t throws that each scored 2 points and f throws that each scored 5 points. If Tia's total score was 37 points, determine all possible ordered pairs (†, ƒ). 3 (c) Since Tia's total score was 37 points, then 2t +5f = 37. Since 2t is even for all integer values of f, then 5f must be odd since their sum is odd). The value of 5f is odd exactly when f is odd. When f = 1, we get 2f + 5 = 37 or 2f = 32. and so f = 16. When f = 3, we get 2 + 15 = 37 or 24 = 22, and so f = 11. When f = 5, we get 21 + 25 = 37 or 2 = 12, and so f = 6. When f = 7, we get 2f + 35 - 37 or 2f = 2, and so t = 1. When ƒ ≥ 9, 5ƒf > 45 and so 2t + 5ƒ > 37. The possible ordered pairs (2. f) are (16, 1), (11,3), (6,5), and (1,7). s 37 (which
Transcribed Image Text:1. 4·3······2·······1· · · · · · · 0······1· · · · · · ·2······3· · · · · · 4 · · · · · · · 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. (c) Tia had t throws that each scored 2 points and f throws that each scored 5 points. If Tia's total score was 37 points, determine all possible ordered pairs (†, ƒ). 3 (c) Since Tia's total score was 37 points, then 2t +5f = 37. Since 2t is even for all integer values of f, then 5f must be odd since their sum is odd). The value of 5f is odd exactly when f is odd. When f = 1, we get 2f + 5 = 37 or 2f = 32. and so f = 16. When f = 3, we get 2 + 15 = 37 or 24 = 22, and so f = 11. When f = 5, we get 21 + 25 = 37 or 2 = 12, and so f = 6. When f = 7, we get 2f + 35 - 37 or 2f = 2, and so t = 1. When ƒ ≥ 9, 5ƒf > 45 and so 2t + 5ƒ > 37. The possible ordered pairs (2. f) are (16, 1), (11,3), (6,5), and (1,7). s 37 (which
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