Evelyn set up 15 rows of chairs in the cafeteria for her school's talent competition. In the first 10 rows, she set up 30 chairs on the left side of the middle aisle and x chairs on the right side. In the last 5 rows, she set up 20 chairs on the left side of the middle aisle and y chairs on the right side to make room for the sound crew.
Pick all the expressions that represent how many chairs Evelyn set up.
(300+10x)+(100+5y)
30(x+10)+20(y+5)
10(30+x)+5(20+y)
x(10+30)+y(5+20)
To find the correct expression, we need to count the total number of chairs set up based on the information provided. We have two different sections: the first 10 rows and the last 5 rows, each with a different arrangement of chairs.
For the first 10 rows, there are 30 chairs on the left and x chairs on the right in each row.
For the last 5 rows, there are 20 chairs on the left and y chairs on the right in each row.
The total number of chairs is therefore the sum of chairs in the first 10 rows and the chairs in the last 5 rows.
Let's analyze each expression to determine which ones correctly represent the total number of chairs:
1. (300+10x)+(100+5y)
This expression calculates (30 chairs × 10 rows) + (10 rows × x chairs on the right) for the first part, which correctly represents the chairs in the first 10 rows. The second part calculates (20 chairs × 5 rows) + (5 rows × y chairs on the right), which correctly represents the chairs in the last 5 rows. This expression is correct.
2. 30(x+10)+20(y+5)
This expression is not correct because it's essentially saying there are x+10 rows of chairs on one side and y+5 rows on the other side, which is not the case. We should be multiplying the number of rows by the number of chairs per row, not adding them.
3. 10(30+x)+5(20+y)
This expression says (30 chairs + x chairs) multiplied by 10 rows for the first part, which correctly represents the chairs in the first 10 rows. The second part says (20 chairs + y chairs) multiplied by 5 rows, which correctly represents the chairs in the last 5 rows. This expression is correct.
4. x(10+30)+y(5+20)
This expression incorrectly interprets the problem. It is as if x chairs are set up for 40 rows and y chairs are set up for 25 rows on the right side, which does not match the scenario provided.
So, the correct expressions that represent how many chairs Evelyn set up are:
(300+10x)+(100+5y)
10(30+x)+5(20+y)