The shamrock inn offers two holiday weekend specials. The first 2 nights and 4 meals for $205, while the other is 3 nights and 8 meals for $342.50. At these rates, what is the room rate and cost of a meal?

The answer to your question is Night = $ 67.5, meal = $17.5

Step-by-step explanation:

Data

Night = n

Meal = m

2n + 4m = $205 (I)

3n + 8m = $342.5 (II)

Process

1. - Solve the system of equations by elimination

Multiply equation I by (3) and equation II by (-2)

6n + 12m = 615

-6n - 16m = - 685

Sum the equations

0 - 4m = - 70

m = - 70 / - 4

m = 17.5

2. - Find the value of n, substitute m in equation I

2n + 4 (17.5) = 205

2n + 70 = 205

2n = 205 - 70

2n = 135

n = 135 / 2

n = 67.5