+120 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? I am soooo confused
Let the cost of Hotel per night=n
Let the cost of car rental per day=r
3n + 4r =675
4n + 5r =875
Solve the following system:
{3 n+4 r = 675 | (equation 1)
4 n+5 r = 875 | (equation 2)
Swap equation 1 with equation 2:
{4 n+5 r = 875 | (equation 1)
3 n+4 r = 675 | (equation 2)
Subtract 3/4 × (equation 1) from equation 2:
{4 n+5 r = 875 | (equation 1)
0 n+r/4 = 75/4 | (equation 2)
Multiply equation 2 by 4:
{4 n+5 r = 875 | (equation 1)
0 n+r = 75 | (equation 2)
Subtract 5 × (equation 2) from equation 1:
{4 n+0 r = 500 | (equation 1)
0 n+r = 75 | (equation 2)
Divide equation 1 by 4:
{n+0 r = 125 | (equation 1)
0 n+r = 75 | (equation 2)
Collect results:
Answer: | n = $125 and r=$75
