happypug2009
Answered

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On the JV baseball team, the number of sophomores is four more than twice the number of freshmen. If there are 16 players combined on the team, how many of each grade level are there?

Sagot :

semsee45

Answer:

4 freshman

12 sophomores

Step-by-step explanation:

Define the variables:

  • Let x = number of sophomores.
  • Let y = number of freshman.

Given information:

  • A total of 16 players on the team.
  • The number of sophomores is four more than twice the number of freshmen.

Create two equations using the defined variables and the given information:

[tex]\textsf{Equation 1}: \quad x+y=16[/tex]

[tex]\textsf{Equation 2}: \quad x=2y+4[/tex]

Substitute Equation 2 into Equation 1 and solve for y:

[tex]\implies (2y+4)+y=16[/tex]

[tex]\implies 3y+4=16[/tex]

[tex]\implies 3y+4-4=16-4[/tex]

[tex]\implies 3y=12[/tex]

[tex]\implies 3y \div 3=12 \div 3[/tex]

[tex]\implies y=4[/tex]

Therefore, there are 4 freshman.

Substitute the found value of y into Equation 1 and solve for x:

[tex]\implies x+4=16[/tex]

[tex]\implies x+4-4=16-4[/tex]

[tex]\implies x=12[/tex]

Therefore, there are 12 sophomores.

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