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

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