✔ 最佳答案
題目1.
設蘋果味糖果之重量為x公斤,橙味糖果之重量為y公斤。
x + y = 40 ..............................[1]
1.5 (40x + 60y) = 81 (x + y) .....[2]
From [1], x = 40 - y .................[3]
Put [3] into [2],
1.5[40(40-y)] + 1.5(60y) = 81[(40-y)+y)]
1.5(1600-40y) + 90y = 81(40)
2400-60y+90y = 3240
30y = 840
y = 28
Put y=28 into [1]
x + 28 = 40
x = 12
∴ 蘋果味糖果之重量為12公斤,橙味糖果之重量為28公斤。
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題目2.
設原來的分數之分子為x,其分母為y。
(x-1)/(y-1) = 1/2 ..........[1]
(x+2)/(y+2) = 2/3 ........[2]
From [1],
2(x-1) = y-1
2x-2 = y-1
y = 2x-1 ....................[3]
Put [3] into [2],
(x+2)/[(2x-1)+2] = 2/3
3(x+2) = 2(2x+1)
3x+6 = 4x+2
-x = -4
x = 4
Put x=4 into [1],
(4-1)/(y-1) = 1/2
3/(y-1) = 1/2
6 = y-1
y = 7
∴ 原來的分數是 4/7 (七分之四)。
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題目3.
設原來的兩位數之十位數字為x,其個位數字為y.
原來的兩位數數值 = 10x+y
現在的兩位數數值 = 10y+x
x + y = 7 .............................[1]
(10y+x) - (10x+y) = 45...........[2]
From [1], x = 7 - y ................[3]
Put [3] into [2],
[10y+(7-y)] - [10(7-y)+y] = 45
(9y +7) - (70-10y+y) = 45
(9y +7) - (70-9y) = 45
9y+7-70+9y = 45
18y-63 = 45
18y = 45+63
18y = 108
y = 6
Put y = 6 into [1],
x + 6 = 7
x = 1
∴原來的兩位數是16。