Question

Y varies as the sum of two quantities, p and q. P varies directly as x and q varies inversely as x. If, y = 19 3 when x = 6 and y = 33 4 when x = 8, what is y when x = 10?

Answer 1

Answer: $\frac{51}{5}$, or 10.2.

Breakdown:

Given: $y = Px + \frac{Q}{x}$

If x = 6, y = 19/3: $\frac{19}{3} = 6P + \frac{Q}{6}$

Or: $38 = 36P + Q$

If x = 8, y = 33/4: $\frac{33}{4} = 8P + \frac{Q}{8}$

Or: $66 = 64P + Q$

Solving, we get:

$P = 1, Q = 2$

Now, $y = 1.x + \frac{2}{x}$

Putting x = 10, we get:

$y = 10 + \frac{2}{10} = 10 + \frac{1}{5} = \frac{51}{5}$