Q:

Brenda and her best friend went on a vacation together. They both paid for a flight, and Brenda had a fancy room for $150 per night, for a total of $1,500. Her friend had a smaller room for $120 per night, for a total of $1,320.Part AWrite and solve a system of linear equations to find the cost of the flight, x, and the number of nights on their vacation, y. Complete the equation for Brenda's costs first.______x + ______y = _____________x + ______y = _______The flights were $___ each, and they stayed ___nights.Part BIf a third friend joined them and stayed in a mid-range room for $130 per night, how much would her vacation cost?

Accepted Solution

A:
Answer:A. 2x + 150y = 1,500    2x + 120y = 1,320The flights were $300 each, and they stayed 6 nights.B. $1,380Step-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]Hence2x + 150y = 1,5002x + 120y = 1,320The 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]