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### Solving a System of Equations: Vidor High School Band Players ###

In the Vidor High School Band, the number of trumpet players is four times that of the French horn players, with a total of 35 musicians. By defining variables for trumpet (T) and French horn (F) players, we can establish a system of equations: T + F = 35 and F = 4T. Using the substitution method, we replace F in the first equation to derive T + 4T = 35, leading us to T = 7 and F = 28. Therefore, there are 7 trumpet players and 28 French horn players in the band. ###

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### Solving a System of Equations: Vidor High School Band Players ###

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  1. Solving A System of Equations Jose MuÑiz(Rolly) & Marycarmen Soto December 18, 2013 (7-8 A)

  2. Problem Situation • In the Vidor High School Band, the number of trumpet players is four times the number of French horn players. • There are 35 trumpet and French horn players in the band. • How many people play the trumpet and how many play the French horn?

  3. Define Variables • T represents the number of trumpet players. • F represents the number of French horn players.

  4. System of Equations • T + F = 35 F = 4T

  5. Solution Method • The method we will be using to solve this problem is substitution. • We will substitute 4T in for the variable F in the first equation.

  6. Step _1_ of Solution • The first step we will be doing is creating an equation. • Read the question multiple times to make sure you have gotten all the information. • Substitute in our system of equations to get one equation with one variable: • T + F = 35 • F = 4T T + 4T = 35 • 5T = 35 • T = 7

  7. Step _2_ of Solution • Since T is equal to 7, replace T with 7 in the second equation. • F = 4 ( 7 ) • F = 28

  8. Solution to the System of Equations • (F, T) • (28, 7)

  9. Check of Solution • 7 + 28 = 35 ☺ • 28 = 4*7 ☺

  10. Solution in the Problem Situation • There are 28 French horn players. • There are 7 trumpet players.

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