Answer:
(a) 160 Naira
(b) Undefined
Step-by-step explanation:
Given
Let:
[tex]y \to[/tex] cost of bag of rice
[tex]x \to[/tex] people demanding the bag
So, we have:
[tex]y\ = \frac{k}{\sqrt x} + c[/tex] ---- The variation
[tex]y = 100; x = 36[/tex]
[tex]y = 150; x = 144[/tex]
We have:
[tex]y\ = \frac{k}{\sqrt x} + c[/tex]
When: [tex]y = 100; x = 36[/tex]
[tex]100 = \frac{k}{\sqrt {36}} + c[/tex]
[tex]100 = \frac{k}{6} + c[/tex] -- (1)
When: [tex]y = 150; x = 144[/tex]
[tex]150 = \frac{k}{\sqrt {144}} + c[/tex]
[tex]150 = \frac{k}{12} + c[/tex]--- (2)
Subtract (1) from (2)
[tex]150 - 100 = \frac{k}{12} - \frac{k}{6} + c - c[/tex]
[tex]50 = \frac{k}{12} - \frac{k}{6}[/tex]
Multiply through by 12
[tex]600 = k - 2k[/tex]
[tex]600 = -k[/tex]
[tex]k = -600[/tex]
To solve for x, we have:
[tex]100 = \frac{k}{6} + c[/tex] -- (1)
This gives:
[tex]100 = \frac{-600}{6} + c[/tex]
[tex]100 = -100 + c[/tex]
[tex]c = 100 + 100[/tex]
[tex]c = 200[/tex]
So, the equation is:
[tex]y\ = \frac{k}{\sqrt x} + c[/tex]
[tex]y = -\frac{600}{\sqrt x} + 200[/tex]
Solving (1): y; when x = 225
We have:
[tex]y = -\frac{600}{\sqrt x} + 200[/tex]
[tex]y = -\frac{600}{\sqrt {225}} + 200[/tex]
[tex]y = -\frac{600}{15} + 200[/tex]
[tex]y = -40 + 200[/tex]
[tex]y = 160[/tex]
Solving (2): x; when x = 200
We have:
[tex]y = -\frac{600}{\sqrt x} + 200[/tex]
[tex]200 = -\frac{600}{\sqrt x} + 200[/tex]
Collect like terms
[tex]\frac{600}{\sqrt x} = 200 - 200[/tex]
[tex]\frac{600}{\sqrt x} =0[/tex]
Cross multiply
[tex]600 =0 * \sqrt x[/tex]
[tex]600 =0[/tex]
x is undefined
