Solve x is partly constant and partly varies as y when y is 10 x is 24 and when y is 14 x is 36 find x when y is 5

Answer 1

To solve this problem, we need to determine the relationship between x and y. We are given that x is partly constant and partly varies with y. Let's denote the constant part as c and the variable part as k.

We can write the expression for x as follows:
x = c + k*y

Using the given information:
When y is 10, x is 24: 24 = c + 10k
When y is 14, x is 36: 36 = c + 14k

Now, let's solve these two equations simultaneously to find the values of c and k.

Start by subtracting the first equation from the second equation:
36 - 24 = (c + 14k) - (c + 10k)
12 = 4k

Divide both sides by 4:
k = 12/4
k = 3

Now substitute the value of k back into the first equation to solve for c:
24 = c + 10*3
24 = c + 30
c = 24 - 30
c = -6

Therefore, the equation for x in terms of y is:
x = -6 + 3y

To find x when y is 5, substitute y = 5 into the equation:
x = -6 + 3*5
x = -6 + 15
x = 9

Thus, when y is 5, x is 9.