Find the value of p if \(\frac{1}{4}\)p + 3q = 10 and 2p – q = 7
-
4
- 3
- -3
- -4
The correct answer is: A
Explanation
\(\frac{1}{4}\)p + 3p = 10...(1)2p - \(\frac{1}{3}\)q = 7...(2)
Multiply equation (2) by 3 to clear fraction
3 x 2p - 3 x \(\frac{1}{3}\)q = 3 x 7
6p - q = 21
6p - 21 = q....(3)
substituting 6p - 21 for q in (1)
\(\frac{1}{4}\)p + 3(6p - 21) = 10...(4)
Multiply equation (4) by 4 to clear fraction
4 x \(\frac{1}{4}\)p + 4 x 3(6p - 21) = 4 x 10
p + 12(6p - 21) = 40
p + 72p - 252
73p = 292
p = \(\frac{292}{73}\)
= 4