If
Q
P
=
S
R
=
U
T
=
4
3
, then what is the value of (4P+5R+7T):(3Q+4S+7U)?
- A12:19
- B6:7
- C3:4
- D5:8
Solution & Step-by-step Explanation
Let P=3k, R=3k, T=3k and Q=4k, S=4k, U=4k.
We need to find the ratio:
3Q+4S+7U
4P+5R+7T
Substitute the values:
=
3(4k)+4(4k)+7(4k)
4(3k)+5(3k)+7(3k)
=
4k(3+4+7)
3k(4+5+7)
=
4k×14
3k×16
=
56k
48k
=
7
6
Correction Note based on standard ratio properties: If the coefficients of the terms were identical in both numerator and denominator (e.g., 4P+5R+7T:4Q+5S+7U), the ratio would remain 3:4. However, given the exact question text coefficient set, evaluating with P=3,Q=4,R=3,S=4,T=3,U=4:
Numerator=4(3)+5(3)+7(3)=12+15+21=48
Denominator=3(4)+4(4)+7(4)=12+16+28=56
Ratio=
56
48
=
7
6
We need to find the ratio:
3Q+4S+7U
4P+5R+7T
Substitute the values:
=
3(4k)+4(4k)+7(4k)
4(3k)+5(3k)+7(3k)
=
4k(3+4+7)
3k(4+5+7)
=
4k×14
3k×16
=
56k
48k
=
7
6
Correction Note based on standard ratio properties: If the coefficients of the terms were identical in both numerator and denominator (e.g., 4P+5R+7T:4Q+5S+7U), the ratio would remain 3:4. However, given the exact question text coefficient set, evaluating with P=3,Q=4,R=3,S=4,T=3,U=4:
Numerator=4(3)+5(3)+7(3)=12+15+21=48
Denominator=3(4)+4(4)+7(4)=12+16+28=56
Ratio=
56
48
=
7
6