Compound Inequalities:
1. Radio stations A and B are 100km apart. The broadcast ranges of station A and station B are 45 km and 30km respectively. Tommy is driving from station A to station B at 50km/h, After travelling t minutes from station A, Tommy cannot hear any broadcasting from station A or station B. Find the range of the possible values of t.
2.A painter can choose to be paid in any one of the following three ways:
(A) $1000, plus $60 per hour
(B) $1500, plus $40 per hour
(C) $80 per hour
Suppose a job takes n hours. Find the range of the possible values of n such the at the painter will earn most money by choosing (A).
3.John is now x years old. Andy is 4 years younger than John, while Peter is 3 years older than John. 7 years ago, their total age was less than 29. 4 years later, their total age will be greater than 56. Find the possible value of x if x is an integer.
拜托解一解。
一些數學問題想請解答
2015-02-10 2:49 am
回答 (2)
2015-02-10 7:43 am
✔ 最佳答案
1.After t minutes:
Distance between the car and station A = 50 × (t/60) = 5t/6 km
Distance between the car and station B = [100 - (5t/6)] km = (600 - 5t)/6 km
5t/6 > 45 and (600 - 5t)/6 > 30
5t > 270 and 600 - 5t > 180
t > 54 and -5t > -420
t > 54 and t < 84
Hence, 54 < t < 84
====
2.
Amount earned by choosing (A) = $(1000 + 60n)
Amount earned by choosing (B) = $(1500 + 40n)
Amount earned by choosing (C) = $80n
When the painter earns most money by choosing (A) :
1000 + 60n > 1500 + 40n and 1000 + 60n > 80n
20n > 500 and 1000 > 20n
n > 25 and 50 > n
Hence, 25 < n < 50
====
3.
Age of John = x
Age of Andy = x - 4
Age of Peter = x + 3
(7 years ago, total ages < 29) and (4 years later, total ages > 56)
(x - 7) + (x - 4 - 7) + (x + 3 - 7) < 29 and (x + 4) + (x - 4 + 4) + (x + 3 +4) > 56
3x - 22 < 29 and 3x + 11 > 56
3x < 51 and 3x > 45
x < 17 and x > 15
15 < x < 17
x is an integer.
Hence, x = 16
2015-02-10 2:53 am
時間有限, 暫只做第三題。
John 現在 x 歲, Andy 比 John 年輕 4 歲, 而 Peter 比 John 年長 3 歲。
七年前, 他們的歲數總和小於 29。四年後, 他們的歲數總和大於 56。
若 x 是整數, 找出 x 的可能值。
解答:
Andy's age now = x - 4
Peter's age now = x + 3
2015-02-09 18:54:58 補充：
7 years ago:
John's age = x - 7
Andy's age = x - 4 - 7 = x - 11
Peter's age = x + 3 - 7 = x - 4
(x - 7) + (x - 11) + (x - 4) < 29
3x - 22 < 29
3x < 51
x < 17
2015-02-09 18:55:38 補充：
4 years later:
John's age = x + 4
Andy's age = x - 4 + 4 = x
Peter's age = x + 3 + 4 = x + 7
(x + 4) + x + (x + 7) > 56
3x + 11 > 56
3x > 45
x > 15
Therefore, from x < 17 and x > 15 and x is an integer, we must have x = 16.
John 現在 x 歲, Andy 比 John 年輕 4 歲, 而 Peter 比 John 年長 3 歲。
七年前, 他們的歲數總和小於 29。四年後, 他們的歲數總和大於 56。
若 x 是整數, 找出 x 的可能值。
解答:
Andy's age now = x - 4
Peter's age now = x + 3
2015-02-09 18:54:58 補充：
7 years ago:
John's age = x - 7
Andy's age = x - 4 - 7 = x - 11
Peter's age = x + 3 - 7 = x - 4
(x - 7) + (x - 11) + (x - 4) < 29
3x - 22 < 29
3x < 51
x < 17
2015-02-09 18:55:38 補充：
4 years later:
John's age = x + 4
Andy's age = x - 4 + 4 = x
Peter's age = x + 3 + 4 = x + 7
(x + 4) + x + (x + 7) > 56
3x + 11 > 56
3x > 45
x > 15
Therefore, from x < 17 and x > 15 and x is an integer, we must have x = 16.
收錄日期: 2021-04-15 18:11:20
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