Theory question 106
Indices(a) If 2x+y = 16 and 4x−y = 1/32, find the values of x and y.
(b) P, Q and R are related in such a way that P ∝ Q2/R. When P = 36, Q = 3 and R = 4. Calculate Q when P = 200 and R = 2.
Show the model answer
Model answer
(a) 2x+y = 24 → x + y = 4. 22(x−y) = 2−5 → x − y = −5/2.
Adding: 2x = 3/2 → x = ¾; y = 4 − ¾ = 3¼.
(b) P = kQ2/R: 36 = 9k/4 → k = 16.
200 = 16Q2/2 → Q2 = 25 → Q = 5 (or −5).
Explanation
Write every number as a power of 2 and equate the indices.