two quantities M and n ARE SUCH THAT m is directly prportional to x. When x=2, their sum is 8 and when x=m their sum is 7. Determine the re;ationship between m and n

Answer 1

Let's assume that the relationship between M and n is given by M = k * n, where k is the constant of proportionality.

According to the problem statement, M is directly proportional to x. This implies that when x doubles, M also doubles.
Therefore, when x = 2, M = 2 * k * n = 2k * n.

We are given that the sum of M and n is 8 when x = 2, so we can write the equation:

2k * n + n = 8

Similarly, when x = M, the sum of M and n is 7. Using our assumption, we can write the equation:

k * n + n = 7

Simplifying both equations, we get:
(2k + 1) * n = 8
(k + 1) * n = 7

Since the left sides of both equations are equal to n, we can equate the right sides:
2k + 1 = k + 1

Solving for k, we find:
k = 0

Now that we have the value of k, we can determine the relationship between M and n:
M = k * n = 0 * n = 0

Therefore, the relationship between M and n is M = 0.