Examination fee is partly constant and varies directly to the number of subject entered. When the examination fee is 550 three subjects are entered. When the examination fee is 700 five subjects are entered. Write the law of variation and find the number of subject entered if the examination fee is 1000

Answer 1

Let x be the constant part of the examination fee and y be the number of subjects entered.

From the problem, we know that:

When y = 3, x + 3k = 550 (where k is the constant of proportionality)
When y = 5, x + 5k = 700

We can solve for x and k by subtracting the first equation from the second:

2k = 150
k = 75

Substituting k back into the first equation:

x + 3(75) = 550
x = 325

So the law of variation is:

examination fee = 325 + 75(number of subjects entered)

To find the number of subjects entered if the examination fee is 1000, we can solve for y:

1000 = 325 + 75y
675 = 75y
y = 9

Therefore, if the examination fee is 1000, the number of subjects entered is 9.