Homework Help is Here – Start Your Trial Now!
Math
Geometry
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). (c) Since Tia's total score was 37 points, then 2t + 5 f = 37. Since 2t is even for all integer values of t, then 5f must be odd since their sum is 37 (which is odd). The value of 5f is odd exactly when f is odd. When f = 1, we get 2t +5= 37 or 2t = 32, and so t = 16. When f = 3, we get 2t +15=37 or 2t = 22, and so t = 11. When f = 5, we get 2t +25= 37 or 2t 12, and so t = 6. When f = 7, we get 2t +35= 37 or 2t = 2, and so t = 1. When f 29, 5f2 45 and so 2t +5f > 37. The possible ordered pairs (t. f) are (16, 1), (11,3), (6,5), and (1,7).

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). (c) Since Tia's total score was 37 points, then 2t + 5 f = 37. Since 2t is even for all integer values of t, then 5f must be odd since their sum is 37 (which is odd). The value of 5f is odd exactly when f is odd. When f = 1, we get 2t +5= 37 or 2t = 32, and so t = 16. When f = 3, we get 2t +15=37 or 2t = 22, and so t = 11. When f = 5, we get 2t +25= 37 or 2t 12, and so t = 6. When f = 7, we get 2t +35= 37 or 2t = 2, and so t = 1. When f 29, 5f2 45 and so 2t +5f > 37. The possible ordered pairs (t. f) are (16, 1), (11,3), (6,5), and (1,7).

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
See similar textbooks
icon
Related questions
Question

In the solution  2t+5x>37, why is it >37?

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). (c) Since Tia's total score was 37 points, then 2t + 5 f = 37. Since 2t is even for all integer values of t, then 5f must be odd since their sum is 37 (which is odd). The value of 5f is odd exactly when f is odd. When f = 1, we get 2t +5= 37 or 2t = 32, and so t = 16. When f = 3, we get 2t +15=37 or 2t = 22, and so t = 11. When f = 5, we get 2t +25= 37 or 2t 12, and so t = 6. When f = 7, we get 2t +35= 37 or 2t = 2, and so t = 1. When f 29, 5f2 45 and so 2t +5f > 37. The possible ordered pairs (t. f) are (16, 1), (11,3), (6,5), and (1,7).
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. (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). (c) Since Tia's total score was 37 points, then 2t + 5 f = 37. Since 2t is even for all integer values of t, then 5f must be odd since their sum is 37 (which is odd). The value of 5f is odd exactly when f is odd. When f = 1, we get 2t +5= 37 or 2t = 32, and so t = 16. When f = 3, we get 2t +15=37 or 2t = 22, and so t = 11. When f = 5, we get 2t +25= 37 or 2t 12, and so t = 6. When f = 7, we get 2t +35= 37 or 2t = 2, and so t = 1. When f 29, 5f2 45 and so 2t +5f > 37. The possible ordered pairs (t. f) are (16, 1), (11,3), (6,5), and (1,7).
AI-Generated Solution
AI-generated content may present inaccurate or offensive content that does not represent bartleby’s views.
steps

Unlock instant AI solutions

Tap the button
to generate a solution

SEE SOLUTION
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Elementary Algebra
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9780998625720
Author:
Lynn Marecek
Publisher:
OpenStax College
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS