✔ 最佳答案
10.
(A) 5
設甲數為 a,乙數為 b。
a = 3b + 4 ... [1]
3a = 5(2b) + 5 ... [2]
將[1]代入[2]中:
3(3b + 4) = 5(2b) + 5
9b + 12 = 10b + 5
b = 7
代入[1]中:
a = 3(7) + 4
a = 25
10(25) ÷ 7 = 35...餘5
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11.
(B) 保特瓶的重量為 50 公克
設保特瓶重 b 公克,汽水原本重 s 克。
b + s = 1850 ... [1]
b + [1 - (1/3)]s = 1250 ... [2]
[1]-[2]:
(1/3)s = 600
s = 1800
代入[1]中:
b + 1800 = 1850
b = 50
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12.
(C) 7
將x=3及y=-2代入[1]中:
3a - 2b = 2 ... [3]
將x=-2及y=2代入[4]中:
-2a + 2b = 2 ... [4]
[3]+[4]:
a = 4
代入[3]中:
3(4) - 2b = 2
b = 5
將x=3及y=-2代入[2]中:
c(3) - 7(-2) = 8
c = -2
a + b + c = 4 + 5 + (-2) = 7
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13.
(B) 17
設白繩長 w 公分,紅繩長 r 公分。
(3/8)w = (1/3)r ... [1]
w + r - (1/3)r = 238 ... [2]
由[1]: w = (8/9)r ... [3]
將[3]代入[2]中:
(8/9)r + r - (1/3)r = 238
(14/9)r = 238
r = 153
代入[1]中:
(3/8)w = (1/3)(153)
w = 136
兩繩長度相差 = 153 - 136 公分 = 17 公分
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14.
(B) 370
設小永原有 w 元,小安原有 n 元。
w = n + 190 ... [1]
(w - 20)/2 = n + 20 + 20 ... [2]
將[1]代入[2]中:
(n + 190 - 20)/2 = n + 40
n + 170 = 2n + 80
n = 90
代入[1]中:
w = 90 + 190
w = 280
小永和小安原共有 = 90 + 280 元 = 370 元
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15.
(D) 7
設十個數字為 t,個位數字為 u。
2t + u = 15 ... [1]
10u + t = 10t + u + 27 ... [2]
由[1]:
u = 15 - 2t ... [3]
將[3]代入[2]中:
10(15 - 2t) + t = 10t + (15 - 2t) + 27
150 - 19t = 8t + 42
t = 4
代入[1]中:
2(4) + u = 15
u = 7
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16.
(A) 20520
設小琳爸、媽去年年終獎金分別為 f 元及 m 元。
f + m = 42000 ... [1]
f(1 + 12%) + m(1 + 8%) = 42000(1 + 10%) + 80 ... [2]
[1]*1.12:
1.12f + 1.12m = 47040 ... [3]
由[2]:
1.12f + 1.08m = 46280 ... [4]
[3]-[4]:
0.04m = 760
m = 19000
媽媽今年年終獎金 = 19000 * (1 + 8%) = 20520
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17.
(C) 7
(3 x 10) ÷ 23 = 1 ... 餘7
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18.
(A) 1/2
設一台甲機器和一台乙機器分別運轉 1 小時產量分別為 a 及 b。
3(4a + 2b) = 2(2a + 5b)
12a + 6b = 4a + 10b
8a = 4b
a = (1/2)b