a hotel offers the following specials: plan a is two nights and one meal for $106. plan b is 2 nights and 4 meals for #130. what price is the hotel charging per night and per meal ??
Let x = nights and y = meals.
2x + 4y = 130
2x + y = 106
Subtract second equation from first.
3y = 24
Solve for y, then put that value into one of the first two equations to find x. To check, put both values in the remaining equation.
$48 per night
$8 per meal
To find the price charged per night and per meal at the hotel, we can set up a system of equations using the given information.
Let's represent the price charged per night as "N" and the price charged per meal as "M".
According to Plan A, two nights and one meal cost $106. So, we can express this as the equation:
2N + 1M = $106 ----------- Equation 1
Similarly, for Plan B, two nights and four meals cost $130. So, we can express this as:
2N + 4M = $130 ----------- Equation 2
Now we have a system of equations with two variables, N and M. We can solve this system to find the values of N and M.
Let's start by eliminating one of the variables. We can do this by multiplying Equation 1 by 4 (to match the coefficient of M in Equation 2) and then subtracting Equation 2 from it.
4(2N + 1M) - (2N + 4M) = 4($106) - $130
8N + 4M - 2N - 4M = $424 - $130
6N = $294
Dividing both sides of the equation by 6:
N = $294 / 6
N ≈ $49
Now we have found the price charged per night, which is approximately $49.
We can substitute this value back into either Equation 1 or Equation 2 to find the price charged per meal.
Using Equation 1:
2($49) + 1M = $106
$98 + M = $106
Subtracting $98 from both sides:
M = $106 - $98
M = $8
Therefore, the hotel charges approximately $49 per night and $8 per meal.