Connor went to New York for vacation. He spent 3 nights at a hotel and rented a car for 4 days. Jillian stayed at the same hotel, but spent 4 nights and rented a car for 5 days from the same company. If Connor paid $675 and Jillian paid $875, how much did one night at the hotel cost?

$75

$100
$125
$150

Question

Connor went to New York for vacation. He spent 3 nights at a hotel and rented a car for 4 days. Jillian stayed at the same hotel, but spent 4 nights and rented a car for 5 days from the same company. If Connor paid $675 and Jillian paid $875, how much did one night at the hotel cost? 

 $75 

 $100 
$125 
$150

anonymous · Answer

Cost of Hotel = H 
Cost of Rent = R 
Days Rented = D 
Nights Rented= N 
How much Paid = P 

So.... 

P = H x N + R x D 

Connor's: 

$675 = H x 3 nights + R x 4 days 

Jillian's: 

$875 = H x 4 nights + R x 5 days 

Solve: 

($675 = H x 3 nights + R x 4 days) x (5) = $3,375 = 15 nights x H + 20 days x R 
($875 = H x 4 nights + R x 5 days) x (-4) = - $3,500 = -16 nights x H + -20 days x R 

$3,375 = 15 nights x H + 20 days x R 
- $3,500 = -16 nights x H + -20 days x R 

-$125 = -1 nights x H 

H = $125

anonymous · Answer

;)