An amount allocated, X will be distributed to households affected by the flood disaster. Given that the distribution calculation formula is that X changes directly with the square of Y and inversely with Z + 3. Given X= 8 000 when Y=80 and Z=47.
(a) Express X in terms of Y and Z.
Accepted Solution
A:
The distribution calculation formula states that:
X is directly proportional to Y^2
X is inversely proportional to Z+3
Using the proportionalities, we can write:
X = k * Y^2 / (Z+3)
where k is a constant of proportionality.
To determine the value of k, we can use the values given in the problem:
X= 8,000, Y = 80, and Z = 47.
Substituting these values into the equation above, we get:
8,000 = k * 80^2 / (47+3)
Simplifying, we get:
8,000 = k * 6400 / 50
k = 8,000 * 50 / 6400
k = 62.5
Now we can substitute this value of k back into the equation:
X = 62.5 * Y^2 / (Z+3)
Therefore, X in terms of Y and Z is:
X = 62.5 * Y^2 / (Z+3)