To find the values of T and M in the given scenario, we can use the concept of direct proportionality. In a direct proportion, two variables (T and M in this case) are related such that their ratio remains constant.
Given:
T is directly proportional to M.
Using the proportionality constant, we can set up the equation:
T = kM,
where k is the proportionality constant.
We can find the value of k by substituting the given values of T and M:
30 = k * 5.
Divide both sides of the equation by 5 to solve for k:
k = 30 / 5 = 6.
Now that we have found the value of k, we can use it to find the requested values:
(a) T when M = 3:
T = kM = 6 * 3 = 18.
Therefore, when M = 3, T = 18.
(b) M when T = 10:
10 = 6M.
Divide both sides of the equation by 6 to solve for M:
M = 10 / 6 = 5/3 ≈ 1.67.
Therefore, when T = 10, M ≈ 1.67.
To summarize:
(a) When M = 3, T = 18.
(b) When T = 10, M ≈ 1.67.