5 N + 2 P = 23
6 N + 3 P = 30
Fill in the blanks.
- 1 N + 1 P = _____
- 1 N = _____
- 1 P = _____
(a)
5 N + 2 P = 23 --- (1)
6 N + 3 P = 30 --- (2)
(2) - (1)
(6 N + 3 P) - (5 N + 2 P) = 30 - 23
6 N - 5 N + 3 P - 2 P = 7
1 N + 1 P = 7 --- (3)
1 N + 1 P = 7
(b)
Make P the same.
LCM of 1 and 2 = 2
(3) x 2
2 N + 2 P = 14 --- (4)
(1) - (4)
(5 N + 2 P) - (2 N + 2 P) = 23 - 14
5 N - 2 N + 2 P - 2 P = 9
3 N = 9
1 N = 9 ÷ 3 = 3
(c)
Substitute 1 N = 3 into (3).
1 N + 1 P = 7
3 + 1 P = 7
1 P = 7 - 3 = 4
Answer(s): (a) 7; (b) 3; (c) 4
