4 P + 2 Q = 28
5 P + 3 Q = 37
Fill in the blanks.
- 1 P + 1 Q = _____
- 1 P = _____
- 1 Q = _____
(a)
4 P + 2 Q = 28 --- (1)
5 P + 3 Q = 37 --- (2)
(2) - (1)
(5 P + 3 Q) - (4 P + 2 Q) = 37 - 28
5 P - 4 P + 3 Q - 2 Q = 9
1 P + 1 Q = 9 --- (3)
1 P + 1 Q = 9
(b)
Make Q the same.
LCM of 1 and 2 = 2
(3) x 2
2 P + 2 Q = 18 --- (4)
(1) - (4)
(4 P + 2 Q) - (2 P + 2 Q) = 28 - 18
4 P - 2 P + 2 Q - 2 Q = 10
2 P = 10
1 P = 10 ÷ 2 = 5
(c)
Substitute 1 P = 5 into (3).
1 P + 1 Q = 9
5 + 1 Q = 9
1 Q = 9 - 5 = 4
Answer(s): (a) 9; (b) 5; (c) 4