Question

write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. aisha, a frequent business traveler, is considering signing up for a hotel rewards program. hotel elegance is currently offering 263 points for signing up, plus 96 points for every night aisha books at the hotel. alternatively, hotel paradiso is offering a sign - up bonus of 262 points, plus 97 points per night. if aisha books a certain number of nights, the points she earns with either hotel will be the same. how many points will she have? how many nights will that be? aisha will have points at either hotel by booking nights.

Explanation:

Step1: Set up equations

Let \( x \) be the number of nights.
For Hotel Elegance: \( y = 263+96x \)
For Hotel Paradiso: \( y = 262 + 97x \)

Step2: Substitute and solve for \( x \)

Since \( y \) is the same for both hotels, set the equations equal:
\( 263+96x=262 + 97x \)
Subtract \( 96x \) from both sides: \( 263=262+x \)
Subtract 262 from both sides: \( x = 1 \)

Step3: Find \( y \)

Substitute \( x = 1 \) into either equation. Using Hotel Elegance's equation: \( y=263 + 96\times1=263 + 96=359 \)

Answer:

Aisha will have \( 359 \) points at either hotel by booking \( 1 \) night.