6 M + 4 N = 62
7 M + 5 N = 74
Fill in the blanks.
- 1 M = _____
- 1 N = _____
- 4 M + 4 N = _____
(a)
6 M + 4 N = 62 --- (1)
7 M + 5 N = 74 --- (2)
Make N the same.
LCM of 4 and 5 = 20
(1) x 5
30 M + 20 N = 310 --- (3)
(2) x 4
28 M + 20 N = 296 --- (4)
(a)
(3) - (4)
(30 M + 20 N) - (28 M + 20 N) = 310 - 296
30 M - 28 M + 20 N - 20 N = 14
2 M = 14
1 M = 14 ÷ 2 = 7
(b)
Substitute M = 7 into (1).
6 M + 4 N = 62
6 x 7 + 4 N = 62
42 + 4 N = 62
4 N = 62 - 42 = 20
1 N = 20 ÷ 4 = 5
(c)
4 M + 4 N
= 4 x 7 + 4 x 5
= 28 + 20
= 48
Answer(s): (a) 7; (b) 5; (c) 48
