Given that y varies as the sum of two quantities one of which
varies as x directly, the other as x inversely, and that y=4
when x=1, and y=5 when x=2, find the equation between
x and y.
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2
Answer:
yαx & yα
x
1
⇒
y=ax+
x
b
if y=6 when x=4
⇒6=4a+
4
b
⇒
16a+b=24
...(1)
& y=10/3 when x=3
⇒
3
10
=3a+
3
b
⇒
9a+b=10
...(2)
Solving (1) & (2) we get ((1)-(2))
7a=14⇒
a=2
∴
b=−8
Hence
y=2x−
x
8
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