Question

1. reasoning eric is planning an event at a hotel. let g stand for the number of eric’s guests. the two expressions represent the difference between the cost of the rooms. expression 1: (326 + 37g) − (287 + 23g). expression 2: 39 + 14g. what can you tell about expression 2 and expression 1?

hotel
function rooms
ocean
booking fee $326
price per guest $37
harbor
booking fee $287
price per guest $23

Explanation:

Step 1: Simplify Expression 1

We start with the given Expression 1 \((326 + 37g)-(287 + 23g)\). By applying the rule of subtracting a sum (distributive property of subtraction), we break it down into \(326+37g - 287-23g\). Then we combine the constant terms (\(326 - 287\)) and the terms with \(g\) (\(37g-23g\)) separately.

Step 2: Compare with Expression 2

After simplifying Expression 1, we get \(39 + 14g\), which is the same as Expression 2 (\(39+14g\)). So, we can say that Expression 1 and Expression 2 are equivalent. This implies that both expressions represent the same cost - difference for the hotel rooms for any number of guests \(g\).

Answer:

To analyze the relationship between Expression 1 and Expression 2, we first simplify Expression 1:

Step 1: Simplify Expression 1

Expression 1 is \((326 + 37g)-(287 + 23g)\).
Using the distributive property \(a-(b + c)=a - b - c\), we get:
\(326+37g - 287-23g\)
Combine like - terms:
For the constant terms: \(326 - 287=39\)
For the terms with \(g\): \(37g-23g = 14g\)
So, \((326 + 37g)-(287 + 23g)=39 + 14g\), which is exactly Expression 2.

This means that Expression 1 and Expression 2 are equivalent. In the context of the problem, Expression 1 represents the difference between the cost of two hotel rooms (Ocean and Harbor) for \(g\) guests, and Expression 2 is a simplified form of Expression 1. So, we can conclude that Expression 1 and Expression 2 are equal (they represent the same value for any number of guests \(g\)).