5 N + 2 P = 30
6 N + 3 P = 39
Fill in the blanks.
- 1 N + 1 P = _____
- 1 N = _____
- 1 P = _____
(a)
5 N + 2 P = 30 --- (1)
6 N + 3 P = 39 --- (2)
(2) - (1)
(6 N + 3 P) - (5 N + 2 P) = 39 - 30
6 N - 5 N + 3 P - 2 P = 9
1 N + 1 P = 9 --- (3)
1 N + 1 P = 9
(b)
Make P the same.
LCM of 1 and 2 = 2
(3) x 2
2 N + 2 P = 18 --- (4)
(1) - (4)
(5 N + 2 P) - (2 N + 2 P) = 30 - 18
5 N - 2 N + 2 P - 2 P = 12
3 N = 12
1 N = 12 ÷ 3 = 4
(c)
Substitute 1 N = 4 into (3).
1 N + 1 P = 9
4 + 1 P = 9
1 P = 9 - 4 = 5
Answer(s): (a) 9; (b) 4; (c) 5