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)
Let us evaluate each given expression to see if they represent the total number of chairs that Evelyn set up.
Given:
- In the first 10 rows, there are 30 chairs on the left and x chairs on the right.
- In the last 5 rows, there are 20 chairs on the left and y chairs on the right.
**Expression (300+10x)+(100+5y)**
If we break down this expression:
- (300+10x) would represent the first part for the first 10 rows (30 chairs on the left per row and x chairs on the right per row).
- (100+5y) would represent the second part for the last 5 rows (20 chairs on the left per row and y chairs on the right per row).
For the first 10 rows:
30 chairs * 10 rows = 300 chairs (left side)
x chairs * 10 rows = 10x chairs (right side)
For the last 5 rows:
20 chairs * 5 rows = 100 chairs (left side)
y chairs * 5 rows = 5y chairs (right side)
Now, adding both parts together: (300 + 10x) + (100 + 5y)
This expression correctly represents the total number of chairs set up by Evelyn.
**Expression 30(x+10)+20(y+5)**
If we expand this expression:
30x + 30*10 + 20y + 20*5
This simplifies to:
30x + 300 + 20y + 100
This does not seem to correctly represent the situation because the fixed number of chairs (30 for the first 10 rows and 20 for the last 5 rows) is being incorrectly multiplied by the number of chairs on the right side (x for the first 10 rows and y for the last 5 rows), instead of being multiplied by the number of rows.
**Expression 10(30+x)+5(20+y)**
If we expand this expression:
10*30 + 10x + 5*20 + 5y
This simplifies to:
300 + 10x + 100 + 5y
For the first 10 rows:
30 chairs * 10 rows = 300 chairs (left side)
x chairs * 10 rows = 10x chairs (right side)
For the last 5 rows:
20 chairs * 5 rows = 100 chairs (left side)
y chairs * 5 rows = 5y chairs (right side)
Adding both parts together: 300 + 10x + 100 + 5y
This expression also correctly represents the total number of chairs set up by Evelyn.
To summarize, two expressions represent the total number of chairs Evelyn set up:
- (300+10x)+(100+5y)
- 10(30+x)+5(20+y)
The expression 30(x+10)+20(y+5) does not correctly represent this total.