2條RATIO 既數學問題!!

[匿名]

2013-10-22 8:10 am

1.
Peter bought some 20-cent and 80-cent stamps. the number of 20 cents stamps was 1/3 of the number of 80 cent cents shamps. He then exchanged 20 80-cent stamps for 20 cent stamps. the number of 80 cent stamps became 5/6 of the number of 20 cent stamps. How many 20-cent stamps did Peter buy at first?

2.
Sam and John shared some stamps. If Sam gave 1/4 of his stamps to John, John will have 80 more stamp than Sam. If Sam gave 1/5 of his stamps to John, they will have a equal stamp. How many did Sam have at first?

回答 (1)

賣女孩的火柴

2013-10-22 9:16 am

✔ 最佳答案

1.
Let a and b be the numbers of 20-cent and 80-cent stamps at first respectively.

The number of 20 cents stamps was 1/3 of the number of 80 cent cents stamps:
a = (1/3)b ...... [1]

He then exchanged 20 80-cent stamps for 80 20-cent stamps.
b - 20 = (5/6)(a + 80) ...... [2]

From [1]:
b = 3a ...... [3]

Put [3] into [2]:
3a - 20 = (5/6)(a + 80)
18a - 120 = 5a + 400
13a = 520
a = 40

Ans: Peter bought 40 stamps at first.

2.
Let s and j be the numbers of stamps of Sam and John respectively.

[j + (1/4)s] - [s - (1/4)s] = 80 ...... [1]
j + (1/5)s = s - (1/5)s ...... [2]

From [1]:
j + (1/4)s - s + (1/4)s = 80
j - (1/2)s = 80 ...... [3]

From [2]:
j - (3/5)s = 0 ...... [4]

[3] - [4]:
(1/10)s = 80
s = 800

Ans: Sam had 800 stamps at first.

參考: 賣女孩的火柴

👍 0 👎 0