4 P + 2 Q = 20
5 P + 3 Q = 27
Fill in the blanks.
- 1 P + 1 Q = _____
- 1 P = _____
- 1 Q = _____
(a)
4 P + 2 Q = 20 --- (1)
5 P + 3 Q = 27 --- (2)
(2) - (1)
(5 P + 3 Q) - (4 P + 2 Q) = 27 - 20
5 P - 4 P + 3 Q - 2 Q = 7
1 P + 1 Q = 7 --- (3)
1 P + 1 Q = 7
(b)
Make Q the same.
LCM of 1 and 2 = 2
(3) x 2
2 P + 2 Q = 14 --- (4)
(1) - (4)
(4 P + 2 Q) - (2 P + 2 Q) = 20 - 14
4 P - 2 P + 2 Q - 2 Q = 6
2 P = 6
1 P = 6 ÷ 2 = 3
(c)
Substitute 1 P = 3 into (3).
1 P + 1 Q = 7
3 + 1 Q = 7
1 Q = 7 - 3 = 4
Answer(s): (a) 7; (b) 3; (c) 4
