Question

26,) If y varies inversely as x, and y = 5 as x = 6, find y for the x-value of 10.

Answer 1

3

Explanation:

the initial statement is

y ∝ 1 /x

to convert to an equation multiply by k the constant

of variation

y = k × 1 /x = k /x

to find k use the given condition

y = 5 when x = 6

y = k/ x ⇒ k = y x = 5 × 6 = 30

y = 30 /x

when

x = 10

then

y = 30 /10 = 3

Answer 2

Answer: y = 3

Explanation:

In inverse variation, as one variable increases, the other variable decreases and as one variable decreases, the other increases.

We would introduce a constant of proportionality, k. Therefore,

y = k/x

When y = 5 , x = 6

Therefore,

5 = k/6

Cross multiplying by 6, it becomes

k = 6 × 5 = 30

The expression becomes

y = 30/x

Therefore, when x is 10,

y = 30/10

y = 3