Question

Or

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

Two groups of volunteers are cleaning up the football stadium after the Homecoming game. Volunteers from the Band Booster Club have already cleaned 9 rows of bleachers and will continue to clean at a rate of 9 rows per minute. The leadership class has completed 7 rows and will continue working at 10 rows per minute. Once the two groups get to the point where they have cleaned the same number of rows, they will take a break and decide how to split up the remaining work. How many minutes will each group have cleaned by then? How long will that take?


The groups will each have finished cleaning
rows in
minutes.

Answer 1

The Band Booster Club and the leadership class will each have cleaned 90 rows in 9 minutes.

Step-by-step explanation:

To solve the problem involving two groups of volunteers cleaning up a football stadium, we'll create two equations based on their rates of work and use substitution to find when they will have cleaned the same number of rows.

Let x represent the number of minutes after the Band Booster Club has cleaned 9 rows, and let y represent the total number of rows cleaned by the Band Booster Club at that time. Since the Band Booster Club cleans at a rate of 9 rows per minute, we can write the first equation as:

y = 9x + 9

Similarly, let x also represent the number of minutes after the leadership class has cleaned 7 rows. Given their rate of 10 rows per minute, the second equation for the leadership class is:

y = 10x + 7

To determine when they have cleaned the same number of rows, we set the two equations equal to each other and solve for x:

9x + 9 = 10x + 7
→ 9 = x

Substituting x=9 back into the first equation:

y = 9(9) + 9
→ y = 81 + 9
→ y = 90

Therefore, both groups will each have finished cleaning 90 rows in 9 minutes.