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.
