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. Findx when y=3

Answer 1

A. To find the relationship between x and y, we can set up a system of equations using the given information.

From the first set of data:
x = ky + c
30 = 2k + c

From the second set of data:
x = ky + c
50 = 6k + c

Now, we can solve these two equations simultaneously to find the values of k and c.

Subtract the first equation from the second:
50 = 6k + c
- 30 = -2k - c
20 = 4k
k = 5

Now substitute the value of k back into the first equation:
30 = 2(5) + c
30 = 10 + c
c = 20

Therefore, the relationship between x and y is x = 5y + 20.

B. To find x when y = 3, we can simply substitute y = 3 into the relationship equation we found in part A.

x = 5(3) + 20
x = 15 + 20
x = 35

Therefore, when y = 3, x = 35.