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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. $\newline$ Gymnasts training for an upcoming competition are practicing their routines for balance beam and floor exercise. During morning practice, Rita practiced her beam routine $3$ times and her floor routine $4$ times, which took a total of $15$ minutes. During afternoon practice, she ran through her her beam routine $8$ times and her floor routine $4$ times, which took a total of $20$ minutes. How long is each routine? $\newline$ The beam routine is $\_$ minutes long and the floor exercise is $\_$ minutes long.

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Solve a system of equations using elimination: word problems

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Gymnasts training for an upcoming competition are practicing their routines for balance beam and floor exercise. During morning practice, Rita practiced her beam routine

3

times and her floor routine

4

times, which took a total of

15

minutes. During afternoon practice, she ran through her her beam routine

8

times and her floor routine

4

times, which took a total of

20

minutes. How long is each routine?

\newline

The beam routine is

\_

minutes long and the floor exercise is

\_

minutes long.

Define variables: Step $1$ : Define the variables for the routines. $\newline$ Let $x$ be the time for the beam routine and $y$ be the time for the floor routine.
Write equations: Step $2$ : Write the equations based on the given information. $\newline$ Morning practice: $3x + 4y = 15$ $\newline$ Afternoon practice: $8x + 4y = 20$
Use elimination: Step $3$ : Use elimination to solve the system. $\newline$ Subtract the morning practice equation from the afternoon practice equation: $\newline$ $(8x + 4y) - (3x + 4y) = 20 - 15$ $\newline$ $5x = 5$
Solve for x: Step $4$ : Solve for x. $\newline$ $5x = 5$ $\newline$ $x = 1$
Substitute for y: Step $5$ : Substitute $x = 1$ back into the morning practice equation to solve for y. $3(1) + 4y = 15$ $3 + 4y = 15$ $4y = 12$ $y = 3$

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