A weekend at the beach bay hotel in Florida includes 2 nights and 4 meals for $195. A full week at the hotel includes 7 nights and 10 meals for $650. How much does 1 night and 1 meal cost?

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Answer 1 · 2018-05-12T11:48:58

$1$ $1$ night and $1$ $1$ meal cost $$ 89.38$ $$89.38$

Assumed that charge of meal and night stay is uniform throughout

the week. $:.2 n +4 m= 195.00 (1) , 7 n +10 m= 650.00 (2)$

Multiplying equation (1) by $7$ and equation (2) by $2$ we get,

$:.14 n +28 m= 1365.00 (3) , 14 n +20 m= 1300.00 (4)$

Subtracting equation (4) from equation (3) we get,

$8 m = 65 :. m= 65/8 or m= 8.125$ Putting $m= 8.125$ in

equation (1) we get, $2 n +4*8.125= 195.00$ or

$2 n + 32.50= 195.00 :. 2 n = 195.00-32.50$ or

$2 n = 162.50 :. n = 81.25 :. 1 n +1 m= 81.25+8.125$ or

$1 n +1 m= 89.375 or 1 n +1 m= 89.38 (2 dp)$

$1$ night and $1$ meal cost $$89.38$ [Ans]