If 10A=3B=7C; find A:B:C
- A30:70:21
- B21:70:30
- C70:21:30
- D7:3:10
Solution & Step-by-step Explanation
Let 10A=3B=7C=k.
Then,
A=
10
k
,B=
3
k
,C=
7
k
The ratio A:B:C is:
A:B:C=
10
1
:
3
1
:
7
1
To clear fractions, multiply by the LCM of 10,3, and 7, which is 210:
A:B:C=(
10
1
×210):(
3
1
×210):(
7
1
×210)
A:B:C=21:70:30
Then,
A=
10
k
,B=
3
k
,C=
7
k
The ratio A:B:C is:
A:B:C=
10
1
:
3
1
:
7
1
To clear fractions, multiply by the LCM of 10,3, and 7, which is 210:
A:B:C=(
10
1
×210):(
3
1
×210):(
7
1
×210)
A:B:C=21:70:30