6 M + 3 N = 69
7 M + 4 N = 84
Fill in the blanks.
- 1 M = _____
- 1 N = _____
- 2 M + 2 N = _____
(a)
6 M + 3 N = 69 --- (1)
7 M + 4 N = 84 --- (2)
Make N the same.
LCM of 3 and 4 = 12
(1) x 4
24 M + 12 N = 276 --- (3)
(2) x 3
21 M + 12 N = 252 --- (4)
(a)
(3) - (4)
(24 M + 12 N) - (21 M + 12 N) = 276 - 252
24 M - 21 M + 12 N - 12 N = 24
3 M = 24
1 M = 24 ÷ 3 = 8
(b)
Substitute M = 8 into (1).
6 M + 3 N = 69
6 x 8 + 3 N = 69
48 + 3 N = 69
3 N = 69 - 48 = 21
1 N = 21 ÷ 3 = 7
(c)
2 M + 2 N
= 2 x 8 + 2 x 7
= 16 + 14
= 30
Answer(s): (a) 8; (b) 7; (c) 30