Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Gymnasts training for an upcoming competition are practicing their routines for balance beam and floor exercise. During morning practice, Hazel practiced her beam routine 9 times and her floor routine 2 times, which took a total of 22 minutes. During afternoon practice, she ran through her her beam routine 8 times and her floor routine 2 times, which took a total of 20 minutes. How long is each routine?The beam routine is minutes long and the floor exercise is minutes long.Submit
Question
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Gymnasts training for an upcoming competition are practicing their routines for balance beam and floor exercise. During morning practice, Hazel practiced her beam routine 9 times and her floor routine 2 times, which took a total of 22 minutes. During afternoon practice, she ran through her her beam routine 8 times and her floor routine 2 times, which took a total of 20 minutes. How long is each routine?The beam routine is minutes long and the floor exercise is minutes long.Submit
Solution
Let's denote the time it takes for Hazel to practice her beam routine as B (in minutes) and the time it takes for her to practice her floor routine as F (in minutes).
From the problem, we can write two equations:
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9B + 2F = 22 (This is from the morning practice where Hazel practiced her beam routine 9 times and her floor routine 2 times, which took a total of 22 minutes.)
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8B + 2F = 20 (This is from the afternoon practice where Hazel practiced her beam routine 8 times and her floor routine 2 times, which took a total of 20 minutes.)
To solve this system of equations using elimination, we can subtract the second equation from the first:
(9B + 2F) - (8B + 2F) = 22 - 20 B = 2
Substitute B = 2 into the first equation:
9*2 + 2F = 22 18 + 2F = 22 2F = 22 - 18 2F = 4 F = 4 / 2 F = 2
So, the beam routine is 2 minutes long and the floor exercise is also 2 minutes long.
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