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Find the fourth proportional to 3.5, 7.5, and 6.3.
13.5
11.5
14.5
12.5
13.5
Notice the ratio of the first two terms: 7.5/3.5=15/7. Simply multiply 6.3 by (15/7) to get the answer quickly: 0.9├Ч15=13.5.
Three proportional numbers are provided: a = 3.5, b = 7.5, and c = 6.3.
d=ab├ЧcтАЛ
Notice the ratio of the first two terms: 7.5/3.5=15/7. Simply multiply 6.3 by (15/7) to get the answer quickly: 0.9├Ч15=13.5.
Many students invert the formula, calculating (a├Чb)/c instead of (b├Чc)/a, leading to incorrect results.
Define Proportionality
For four numbers a, b, c, and d to be in proportion, the relation is a:b::c:d, which implies a/b=c/d.
baтАЛ=dcтАЛ
Rearrange for Fourth Proportional
To solve for d, we rearrange the equation: d=(b├Чc)/a.
d=3.57.5├Ч6.3тАЛ
Calculate the Value
Simplify by removing decimals: (75├Ч63)/(35├Ч10)=(15├Ч63)/(7├Ч10)=15├Ч0.9=13.5.
d=13.5
A is correct because the calculated value of the fourth proportional is 13.5.
This concept is foundational for 'Variation' problems in Profit & Loss and Time & Work chapters, where quantities often scale proportionally.
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