8 P + 5 Q = 67
9 P + 6 Q = 78
Fill in the blanks.
- 1 P = _____
- 1 Q = _____
- 5 P + 2 Q = _____
(a)
8 P + 5 Q = 67 --- (1)
9 P + 6 Q = 78 --- (2)
Make Q the same.
LCM of 5 and 6 = 30
(1) x 6
48 P + 30 Q = 402 --- (3)
(2) x 5
45 P + 30 Q = 390 --- (4)
(a)
(3) - (4)
(48 P + 30 Q) - (45 P + 30 Q) = 402 - 390
48 P - 45 P + 30 Q - 30 Q = 12
3 P = 12
1 P = 12 ÷ 3 = 4
(b)
Substitute P = 4 into (1).
8 P + 5 Q = 67
8 x 4 + 5 Q = 67
32 + 5 Q = 67
5 Q = 67 - 32 = 35
1 Q = 35 ÷ 5 = 7
(c)
5 P + 2 Q
= 5 x 4 + 2 x 7
= 20 + 14
= 34
Answer(s): (a) 4; (b) 7; (c) 34
