Respuesta :
Answer:
The beam routine is two (2) minutes long and the floor exercise is one (1) minute long.
Explanation:Let Rosanne's beam routine be represented by x, and the floor routine be represented by y.
Since it took her 3 minutes to complete one of the beam and floor routines, we have:
[tex]x+y=3...............................................(1)[/tex]During her afternoon practice, she ran through her beam routine 4 times and her floor routine 6 times, which took a total of 14 minutes
[tex]4x+6y=14.................................................(2)[/tex](2) may be written as:
[tex]2x+3y=7...............................................(3)[/tex]To know how long each routine is, we solve (1) and (3) simultaneously as follows.
Subtract twice equation (1) from equation (3)
[tex]\begin{gathered} 2x-2x+3y-2y=7-6 \\ y=1 \end{gathered}[/tex]Substitute y = 1 into equation (1)
[tex]\begin{gathered} x+1=3 \\ x=3-1=2 \end{gathered}[/tex]The beam routine, x = 2 minutes long
The floor exercise, y = 1 minute long.
