Answer:
A. 2x + 150y = 1,500
2x + 120y = 1,320
The flights were $300 each, and they stayed 6 nights.
B. $1,380
Step-by-step explanation:
Let x be the cost of the flight (in one side) and y be the number of nights on their vacation.
A. Brenda had a fancy room for $150 per night, then she paid $150y for y nights. Brenda's total is $1,500, then
[tex]150y+2x=1,500[/tex]
Brenda's friend had a smaller room for $120 per night, then she paid $120y for y nights. Brenda's friend total is $1,320, then
[tex]120y+2x=1,320[/tex]
Subtract two equations:
[tex]150y+2x-120y-2x=1,500-1,320\\ \\30y=180\\ \\y=6[/tex]
Substitute into the first equation:
[tex]150\cdot 6+2x=1,500\\ \\900+2x=1,500\\ \\2x=600\\ \\x=300[/tex]
Hence
2x + 150y = 1,500
2x + 120y = 1,320
The flights were $300 each, and they stayed 6 nights.
B. If a third friend joined them and stayed in a mid-range room for $130 per night, then he paid [tex]\$130\cdot 6=\$780[/tex]
The total cost is
[tex]\$780+\$600=\$1,380[/tex]
