算國一數學

2008-04-29 1:06 am
若5:X:6/5=3:1/2:Y 求X Y之值

設4:5:7=6:X:Y 求X= Y=


已之2X:3Y:4Z=1:2:3 且1/X:1/Y:1/Z=6:A:B 求A= 求B=

回答 (2)

2008-04-29 1:24 am
✔ 最佳答案
若5:X:6/5=3:1/2:Y 求X Y之值

3X=5(1/2) ==> X=5/6

5Y = 3(6/5) ==> Y= 18/25

設4:5:7=6:X:Y 求X= Y=

4X = 5*6 = 30 ==> X=7.5

4Y = 7*6 = 42 ==> Y=10.5

已之2X:3Y:4Z=1:2:3 且1/X:1/Y:1/Z=6:A:B 求A= 求B=

2*2X = 1*3Y ==> X = (3/4)Y ==> (1/X):(1/Y) = 4:3 = 6:4.5

3*2X = 1*4Z ==> X = (2/3)Z ==> (1/X):(1/Z) = 3:2 =6:4

所以, (1/X):(1/Y):(1/Z) = 6:4.5:4=6:A:B ==> A=4.5, B=4
2008-04-29 4:43 am
若5:X:6/5=3:1/2:Y 求X Y之值
5:X=3:1/2
3*X=(1/2)*5
3X=5/2
X=(5/2)/3=(5/2)*(1/3)=5/6
5:6/5=3:Y
5*Y=3*(6/5)
5Y=18/5
Y=(18/5)/5=(18/5)*(1/5)=18/25=0.72

答案:X=5/6;Y=0.72

設4:5:7=6:X:Y 求X= Y=
4:5=6:X
4*X=6*5
4X=30
X=30/4=7.5
4:7=6:Y
4*Y=7*6
4Y=42
Y=42/4=21/2=10.5

答案:X=7.5;Y=10.5

已之2X:3Y:4Z=1:2:3 且1/X:1/Y:1/Z=6:A:B 求A= 求B=
2X:3Y=1:2
2*2X=3Y*1
Y=(4/3)X
1/Y=1/[(4/3)X]=(3/4)*(1/X)
2X:4Z=1:3
4Z*1=2X*3
4Z=6X
Z=(6/4)X=(3/2)X
1/Z=1/[(3/2)X]=(2/3)*(1/X)
1/X:1/Y:1/Z=1/X:[(3/4)*(1/X)]:[(2/3)*(1/X)]=1:(3/4):(2/3)=12:9:8
12:9:8=6:A:B
12:9=6:A
12*A=6*9
12A=54
A=54/12=9/2=4.5
12:8=6:B
12*B=8*6
12B=48
B=48/12=4

答案:A=4.5;B=4
參考: Me算


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