X is partly constant and partly varies as y when y=2, x=30 and when y=6, x=50.

Question

A) find the relationship between x and y
B) find x when y=3

Answer 1

A) We can start by finding the constant part of x. We do this by setting y=2 and y=6 and solving for the corresponding values of x:

When y=2, x=30
When y=6, x=50

The difference between these two values of x is 20. This means that the part of x that varies with y changes by 20 when y increases from 2 to 6. To find the relationship between x and y, we can set up a proportion:

(change in x) / (change in y) = (part of x that varies) / y

Plugging in the values we know, we get:

20 / (6-2) = (part of x that varies) / 6

Solving for the part of x that varies, we get:

(part of x that varies) = 20/4 = 5

Therefore, the relationship between x and y is:

x = 5y + C, where C is the constant part of x.

To find the value of C, we can plug in one of the known values for x and y:

30 = 5(2) + C

Solving for C, we get:

C = 20

So the complete relationship between x and y is:

x = 5y + 20

B) To find x when y=3, we can plug in y=3 into the equation we just found:

x = 5(3) + 20 = 35

Therefore, when y=3, x=35.