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A hotel has a total of 315 rooms that come in two sizes: Single and Double. The hotel has 75 more single rooms as it does double rooms. How many of each type does the hotel have?

Respuesta :

MrRoyal

Answer:

195 single rooms and 120 double rooms

Step-by-step explanation:

Given

Represent the single room with S and the double with D.

[tex]S = 75 + D[/tex] --- 75 more single rooms

[tex]S + D = 315[/tex] --- Total number of rooms

Required

Find the number of each room

Substitute 75 + D for S in [tex]S + D = 315[/tex]

[tex]75 + D + D = 315[/tex]

[tex]75 + 2D = 315[/tex]

Collect Like Terms

[tex]2D = 315 - 75[/tex]

[tex]2D = 240[/tex]

Make D the subject

[tex]D = \frac{240}{2}[/tex]

[tex]D = 120[/tex]

Substitute 120 for D in [tex]S = 75 + D[/tex]

[tex]S = 75 + 120[/tex]

[tex]S = 195[/tex]

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