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If the fourth proportional to 4, 8, and 10 is y, find y.
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20
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20
Notice the ratio of the first two numbers: 8/4=2. Therefore, the fourth proportional is simply 10├Ч2=20.
Three numbers are given: 4, 8, and 10. We need to find the fourth proportional y.
baтАЛ=ycтАЛтЯ╣y=ab├ЧcтАЛ
Notice the ratio of the first two numbers: 8/4=2. Therefore, the fourth proportional is simply 10├Ч2=20.
Many students mistake the order and calculate y=(a├Чb)/c instead of (b├Чc)/a, or try to find the third proportional instead of the fourth.
Define the relationship
By definition of the fourth proportional, if a,b,c,y are in proportion, then a:b::c:y.
4:8=10:y
Set up the equation
Convert the ratio into a fraction: 84тАЛ=y10тАЛ.
y=48├Ч10тАЛ
Calculate the final value
Simplify the expression to find y: y=80/4=20.
y=20
B is correct because the calculation y=(8├Ч10)/4 results in 20.
This concept is a precursor to understanding 'Direct Variation' in physics, where y=kx and constant k is determined by proportionality.
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