Solved on Dec 06, 2023

Beach clean-up volunteers collected 1.5 more pounds per person this year. With 80 volunteers, they removed 360 pounds total. Find the average amount of trash collected per volunteer last year using the equation: $1.5x + 80 = 360$ .

STEP 1

Assumptions
1. There were 80 volunteers this year.
2. Together, they collected 360 pounds of trash.
3. Each volunteer collected an average of 1.5 more pounds of trash this year compared to last year.
4. We are looking for an equation to find $x$ , the average amount of trash collected per volunteer last year.

STEP 2

Let's denote $x$ as the average amount of trash collected by each volunteer last year. This year, each volunteer collected $x + 1.5$ pounds of trash on average.

STEP 3

Since there were 80 volunteers this year, and they each collected $x + 1.5$ pounds on average, the total amount of trash collected this year can be represented as $80(x + 1.5)$ .

STEP 4

We know that the total amount of trash collected this year is 360 pounds. Therefore, we can set up the equation:
$80(x + 1.5) = 360$

STEP 5

To confirm that this is the correct equation, we can check the dimensions of each term. The left side of the equation represents the total pounds of trash collected (number of volunteers times the average pounds per volunteer), and the right side represents the total pounds of trash collected as given in the problem statement. Both sides have the dimension of pounds, which is consistent.

STEP 6

None of the other equations provided correctly represent the situation described:
- The equation $80x + 1.5 = 360$ suggests that only an additional 1.5 pounds total was collected this year, which is not consistent with the problem statement. - The equation $1.5(x + 80) = 360$ incorrectly distributes the 1.5 pounds across the sum of the average trash collected last year and the number of volunteers. - The equation $1.5x + 80 = 360$ does not account for the total number of volunteers this year and incorrectly adds 80 to the product of 1.5 and $x$ .

STEP 7

Thus, the correct equation to find $x$ , the average amount of trash collected by each volunteer last year, is:
$80(x + 1.5) = 360$

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Beach clean-up volunteers collected 1.5 more pounds per person this year. With 80 volunteers, they removed 360 pounds total. Find the average amount of trash collected per volunteer last year using the equation: $1.5x + 80 = 360$ .

STEP 1

STEP 2

Let's denote $x$ as the average amount of trash collected by each volunteer last year. This year, each volunteer collected $x + 1.5$ pounds of trash on average.

STEP 3

Since there were 80 volunteers this year, and they each collected $x + 1.5$ pounds on average, the total amount of trash collected this year can be represented as $80(x + 1.5)$ .

STEP 4

We know that the total amount of trash collected this year is 360 pounds. Therefore, we can set up the equation:
$80(x + 1.5) = 360$

STEP 5

STEP 6

STEP 7

Thus, the correct equation to find $x$ , the average amount of trash collected by each volunteer last year, is:
$80(x + 1.5) = 360$

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Beach clean-up volunteers collected 1.5 more pounds per person this year. With 80 volunteers, they removed 360 pounds total. Find the average amount of trash collected per volunteer last year using the equation: 1.5x+80=3601.5x + 80 = 3601.5x+80=360.

STEP 1

STEP 2

Let's denote xxx as the average amount of trash collected by each volunteer last year. This year, each volunteer collected x+1.5x + 1.5x+1.5 pounds of trash on average.

STEP 3

Since there were 80 volunteers this year, and they each collected x+1.5x + 1.5x+1.5 pounds on average, the total amount of trash collected this year can be represented as 80(x+1.5)80(x + 1.5)80(x+1.5).

STEP 4

We know that the total amount of trash collected this year is 360 pounds. Therefore, we can set up the equation:80(x+1.5)=36080(x + 1.5) = 36080(x+1.5)=360

STEP 5

STEP 6

STEP 7

Thus, the correct equation to find xxx, the average amount of trash collected by each volunteer last year, is:80(x+1.5)=36080(x + 1.5) = 36080(x+1.5)=360

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Beach clean-up volunteers collected 1.5 more pounds per person this year. With 80 volunteers, they removed 360 pounds total. Find the average amount of trash collected per volunteer last year using the equation: $1.5x + 80 = 360$ .

Let's denote $x$ as the average amount of trash collected by each volunteer last year. This year, each volunteer collected $x + 1.5$ pounds of trash on average.

Since there were 80 volunteers this year, and they each collected $x + 1.5$ pounds on average, the total amount of trash collected this year can be represented as $80(x + 1.5)$ .

We know that the total amount of trash collected this year is 360 pounds. Therefore, we can set up the equation:
$80(x + 1.5) = 360$

Thus, the correct equation to find $x$ , the average amount of trash collected by each volunteer last year, is:
$80(x + 1.5) = 360$