6 N + 4 P = 44
7 N + 5 P = 53
Fill in the blanks.
- 1 N + 1 P = _____
- 1 N = _____
- 1 P = _____
(a)
6 N + 4 P = 44 --- (1)
7 N + 5 P = 53 --- (2)
(2) - (1)
(7 N + 5 P) - (6 N + 4 P) = 53 - 44
7 N - 6 N + 5 P - 4 P = 9
1 N + 1 P = 9 --- (3)
1 N + 1 P = 9
(b)
Make P the same.
LCM of 1 and 4 = 4
(3) x 4
4 N + 4 P = 36 --- (4)
(1) - (4)
(6 N + 4 P) - (4 N + 4 P) = 44 - 36
6 N - 4 N + 4 P - 4 P = 8
2 N = 8
1 N = 8 ÷ 2 = 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