7 P + 3 Q = 35
8 P + 4 Q = 44
Fill in the blanks.
- 1 P = _____
- 1 Q = _____
- 4 P + 4 Q = _____
(a)
7 P + 3 Q = 35 --- (1)
8 P + 4 Q = 44 --- (2)
Make Q the same.
LCM of 3 and 4 = 12
(1) x 4
28 P + 12 Q = 140 --- (3)
(2) x 3
24 P + 12 Q = 132 --- (4)
(a)
(3) - (4)
(28 P + 12 Q) - (24 P + 12 Q) = 140 - 132
28 P - 24 P + 12 Q - 12 Q = 8
4 P = 8
1 P = 8 ÷ 4 = 2
(b)
Substitute P = 2 into (1).
7 P + 3 Q = 35
7 x 2 + 3 Q = 35
14 + 3 Q = 35
3 Q = 35 - 14 = 21
1 Q = 21 ÷ 3 = 7
(c)
4 P + 4 Q
= 4 x 2 + 4 x 7
= 8 + 28
= 36
Answer(s): (a) 2; (b) 7; (c) 36
