中二簡單simultaneous equation

2009-12-22 6:19 am

1.a hotel can serve 300people for dinner buffet.the price for an adult is $200 and that for a child is %130.if the hotel was full and it received $51600 yesterday,find the respective numbers of adults and children

2.mr.wong has some $20-note and $100-note with a total amount of $920.if he has 14 pieces of notes,find the number of 20$-note and that of 100-note

回答 (1)

用戶9112

2009-12-22 6:25 am

✔ 最佳答案

(1) Let the number of adult and children be x and y respectively
x + y = 300 ... (1)
200x + 130y = 51600 ... (2)
(1) * 200 => 200x + 200y = 60000 ... (3)
(3) - (2) => 70y = 8400
y = 120
Sub into (1), x + 120 = 300 => x = 180
There are 180 adults and 120 children
(2) Let the number of $20 notes and $100 notes be x and y respectively
20x + 100y = 920 ... (1)
x + y = 14 ... (2)
(2) => x = 14 - y ... (3)
Sub into (1), 20(14 - y) + 100y = 920
280 - 20y + 100y = 920
80y = 640
y = 8
Sub into(3), x = 14 - 8 = 6
There are 6 $20 notes and 8 $100 notes.

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