a math problem please help asap?

Question

a special vacation plan advertises 5 nights and 14 meals for $565 or 7 nights and 20 meals for $795. how much is the per night and the per meal charge thanks to all

Answer 1

5 nights and 14 meals for $565 or 7 nights and 20 meals for $795

N = cost per night
M = cost per meal

a) 5N + 14 M = 565
b) 7N + 20 M = 795

mult a by 7, and b by 5 or

a) 35N + 98 M = 3955
b) 35N +100M = 3975, SUBTRACT
-------------------------
- 2M = -20
M = 10 dollars

subs into either

a) 5N + 14 M = 565 becomes
5N + 14 * 10= 565 or
5N + 140 = 565 or
5N = 425 or
N = 85. Done.

Answer 2

Cost per night = N
Cost per meal = M

5N + 14M = 565
7N + 20M = 795

7(5N + 14M) = 7*565
35N + 98M = 3955

5(7N + 20M) = 5*795
35N + 100M = 3975

(35N + 100M) - (35N + 98M) = 3975 - 3955
2M = 20
M = 10

5N + 14(10) = 565
5N = 565 - 140
5N = 425
N = 425/5
N = 85

Cost per night = 85
Cost per meal = 10

CHECK
5 Nights = 85*5 = 425
14 Meals = 10*14 = 140
Total = 425 + 140 = 565

7 Nights = 85*7 = 595
20 Meals = 20*10 = 200
Total = 595 + 200 = 795

Answer 3

Let n=cost of 1 night, m = cost of 1 meal.
5n+14m = 565
7n + 20m = 795

The coefficients of n are 5 and 7. The least common multiple of 5 and 7 is 35, so multiply the first equation by 7 and the second equation by 5,
7(5n+14m = 565) ⇒ 35n + 98m = 3955
5(7n + 20m = 795) ⇒ 35n + 100m = 3975

then subtract one from the other to eliminate n
35n + 100m = 3975
-(35n + 98m = 3955)
---------------------------
35n-35n+100m-98m = 3975-3955
Simplify, solve for m, then plug it back into the first equation and solve for n.

Answer 4

5n +14m =565
7n +20m =795
-35n -98m = - 3955
35n +100m = 3975
2m = 20
m = $10
5n + 14*10 =565
5n = 425 --> n= $85