Question

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 A
Write 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 B
If a third friend joined them and stayed in a mid-range room for $130 per night, how much would her vacation cost?

Answer 1

A. 2x + 150y = 1,500

2x + 120y = 1,320

The flights were $300 each, and they stayed 6 nights.

B. $1,380

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

`150y+2x=1,500`

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

`120y+2x=1,320`

Subtract two equations:

`150y+2x-120y-2x=1,500-1,320\\ \\30y=180\\ \\y=6`

Substitute into the first equation:

`150\cdot 6+2x=1,500\\ \\900+2x=1,500\\ \\2x=600\\ \\x=300`

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
`\$130\cdot 6=\$780`

The total cost is

`\$780+\$600=\$1,380`