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Freshmen and Sophomores Solve by setting up a system of linear equations with 2 variables and 2 unknowns. A total of 1,595 first and second year college students gathered at a pep rally. The number of freshman exceeded the number of sophomores by 15. How many freshmen were at the pep rally? A) There were 790 freshmen at the pep rally. B) There were 795 freshmen at the pep rally. C) There were 800 freshmen at the pep rally. D) There were 805 freshmen at the pep rally.


(PRECAL)

Respuesta :

jcherry99

Let S = the sophomores
Let R = the freshmen
Short Answer C
s + r = 1595   (1)
s + 15 = r      (2)

Substitute for r from equation (2) into equation (1)
s + s + 15 = 1595  Combine like terms
2s + 15 = 1595      Subtract 15 from both sides
2s = 1595 - 15    
2s = 1580              Divide by 2
s = 1580/2
s = 795 sophmores.

s + r = 1595
795 + r = 1595     Subtract 795 from both sides
r = 1594 - 795
r = 800 Freshmen

Answer C <<<<<<
boffeemadrid

The number of freshmen that were at the pep rally is required.

D) There were 805 freshmen at the pep rally.

Let [tex]x[/tex] be the number of Freshmen

and [tex]y[/tex] be the number Sophomores.

Number of freshmen is 15 more than the sophomore.

So,

[tex]x=15+y\\\Rightarrow x-y=15[/tex]

Total number of Freshmen and Sophomores are 1595

The equations are

[tex]x+y=1595[/tex]

[tex]x-y=15[/tex]

Adding the equations we get

[tex]2x=1595+15\\\Rightarrow x=\dfrac{1610}{2}\\\Rightarrow x=805[/tex]

Hence, D) There were 805 freshmen at the pep rally.

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