5 M + 3 N = 39
6 M + 4 N = 48
Fill in the blanks.
- 1 M = _____
- 1 N = _____
- 5 M + 5 N = _____
(a)
5 M + 3 N = 39 --- (1)
6 M + 4 N = 48 --- (2)
Make N the same.
LCM of 3 and 4 = 12
(1) x 4
20 M + 12 N = 156 --- (3)
(2) x 3
18 M + 12 N = 144 --- (4)
(a)
(3) - (4)
(20 M + 12 N) - (18 M + 12 N) = 156 - 144
20 M - 18 M + 12 N - 12 N = 12
2 M = 12
1 M = 12 ÷ 2 = 6
(b)
Substitute M = 6 into (1).
5 M + 3 N = 39
5 x 6 + 3 N = 39
30 + 3 N = 39
3 N = 39 - 30 = 9
1 N = 9 ÷ 3 = 3
(c)
5 M + 5 N
= 5 x 6 + 5 x 3
= 30 + 15
= 45
Answer(s): (a) 6; (b) 3; (c) 45
