Find the amount allowed for a hotel room and daily food expenses?

Question

Corporation Wally Mart allows each of its traveling employees an amount of money per day for a hotel room and food expenses. One employee travels for 4 days and 4 nights and is allotted $480 while another employee travels for 3 days and 2 nights and is allotted $270.

a) Give the system of equations for solving this situation.
b) Find the amount allowed for a hotel room and daily food expenses.

Answer 1

4d + 4n = 480
3d + 2n = 270

Combining...

d = 30
n = 90

Answer 2

Let x = amount allowed for hotel room
Let y = amount allowed for food

4x + 4y = 480 <--- Eq 1
2x + 3y = 270 <--- Eq 2
Multiply Eq 2 by -2 getting:
-4x -6y = -540 <--- Eq 3
Add Eq 3 to Eq 1 getting:
-2y = 60
y = 30 = dollars for food/day
Substitute y= 30 in Eq 2 getting:
2x + 90 =270
2x = 180
x = 90 dollars for hotel/day