3 nights including six meals for $132.00. at that rate, what is the cost of one nights lodging

Question

3 nights including six meals for $132.00

3 nights including two meals for $109.00

At these rates,  what is the cost of one nights lodging. 

Answer 1

Let x = the cost of one night's lodging and y = the cost of one meal:

 

$132 = 3x + 6y

$109 = 3x + 2y

 

Multiply the second equation by -3:

 

-3*($109 = 3x + 2y)

-327 = -9x - 6y

 

Now add this modified equation to the first equation:

 

  $132 =  3x + 6y

-$327 = -9x - 6y

------------------

-$195 = -6x

 

Solve for x, the cost of one night's lodging.

Answer 2

Let N = night rate and M = meal cost

 

3N + 6M = 132

3N + 2M = 109      multiply both sides by -1 and add it 

 

6M - 2M = 132 - 109

 

M = 5.75 , therefore one meal costs $5.75, thus

 

3N + 6(5.75) = 132

 

N = 97.5, therefore, one night rate is $ 97.5