二元一次聯立方程應用題 （中二）

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。

let apple candy be xkg, orange candy candy be y kg
x + y = 40 ..............................[1]
(1+50% )(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

[1],x + 28 = 40
x = 12

∴ let apple candy be 12kg, orange candy candy be 28 kg


2)let the original fraction be x/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

[1],
(4-1)/(y-1) = 1/2
3/(y-1) = 1/2
y=7

∴ the original fraction is 4/7


3)

let the original no. be 10x+y
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
18y = 45+63
y = 6

[1],
x + 6 = 7
x = 1

∴the original no. is 16

No 3 :

{ x+y = 7 ----------(1)
{ 10y+x - (10x+y) = 45 ----------(2)

(1) x+y = 7
y = 7-x ----------------(3)
把(3)代入(2)
10y+x - 10x-y = 45
10(7-x)+x - 10x-(7-x) = 45
70 - 7 - 10x - 10x + x + x =45
63 - 20x + 2x = 45
-18x =63-45
x = 1 ---------------------- (4)
把 (4)代入(1)
x + y = 7
y = 6

x=1 y=6