Question

8o + 12p = 382 12o + 8p = 388 What does p equal?

Answer 1

For this case we have a system of two equations with two variables:

Clear "o" from the first equation:

$8o = 382-12p\\o = \frac {382-12p} {8} = \frac {191-6p} {4}$

We substitute in the second equation:

$12 (\frac {191-6p} {4}) + 8p = 388\\3 (191-6p) + 8p = 388\\573-18p + 8p = 388\\-10p = 388-573\\-10p = -185\\p = \frac {185} {10}\\p = 18.5$

ANswer:

$p = 18.5$

Answer 2

A simpler way...

Multiplying equation no. 1 with 3 and equation no.2 with 2, we substract them.

$240o + 36p = 1146 \\ - 240o - 16p = - 776$

$20p = 370 \\ p = \frac{370}{20 } \\ p = 18.5$