F.3 MATHS!Linear Inequalities

2012-09-18 1:17 am

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1) (1/2)-(x/4) < x+(1/8)
2a) 3[3x+(x-6)/2] < 6(1-2x)
2b) 3[(x-2)/4-(x+2)/6]≦(x-5)/2

3) For two consecutive multiples of 3, 5 times the larger number is not less than 2 times the smaller number plus 45. Find the minimum values of these two numbers.

4) A shopkeeper sells articles A and B. For each article A and article B sold, he can earn $50 and $70 respectively. If the shopkeeper has sold 30 articles, find the minimum number of article B sold when the profit made is at least $1900.

5)According to official basketball rules, a goal made beyond the three-point line counts as 3 points, while a goal made within the three-point line counts 2points, If a basketball team makes 45 goals in a game and their total score is less than 100 points, how many 3-point goals have they made at most? (Assume all the goals the team made are 2-point or 3-point goals)

回答 (1)

micatkie

2012-09-19 8:49 pm

✔ 最佳答案

1)
(1/2) - (x/4) < x + (1/8)
-(x/4) - x < (1/8) - (1/2)
-5x/4 < -3/8
(5/4)x > 3/8
x > (3/8) * (4/5)
x > 3/10

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2a)
3[3x + (x - 6)/2] < 6(1 - 2x)
6[3x + (x - 6)/2] < 12(1 - 2x)
18x + 3x - 18 < 12 - 24x
21x - 18 < 12 - 24x
21x + 24x < 12 + 18
45x < 30
x < 30/45
x < 2/3

2b)
If it is 3[(x - 2)/4 - (x + 2)/6] ≤ (x - 5)/2
3[(x - 2)/4 - (x + 2)/6] * 4 ≤ [(x - 5)/2] * 4
3x - 6 - 2x - 4 ≤ 2x - 10
x - 10 ≤ 2x - 10
x - 2x ≤ -10 + 10
-x ≤ 0
x ≥ 0

If it is 3[(x - 2)/4 - (x + 2)/6] ≥ (x - 5)/2
3[(x - 2)/4 - (x + 2)/6] * 4 ≥ [(x - 5)/2] * 4
3x - 6 - 2x - 4 ≥ 2x - 10
x - 10 ≥ 2x - 10
x - 2x ≥ -10 + 10
-x ≥ 0
x ≤ 0

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4)
Let b be the number of article B sold.
Then, the number of article A sold = 30 - b

50(30 - b) + 70b ≥ 1900
1500 - 50b + 70b ≥ 1900
20b ≥ 400
b ≥ 20

The minimum number of article B sold = 20

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5)
Let n be the number of 3-point goals.
Then, the number of 2-point goals = 45 - n

3n + 2(45 - n) < 100
3n + 90 - 2n < 100
n < 10

The maximum number of 3-point goals = 9

參考: micatkie

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