7 M + 5 N = 81
8 M + 6 N = 94
Fill in the blanks.
- 1 M = _____
- 1 N = _____
- 3 M + 4 N = _____
(a)
7 M + 5 N = 81 --- (1)
8 M + 6 N = 94 --- (2)
Make N the same.
LCM of 5 and 6 = 30
(1) x 6
42 M + 30 N = 486 --- (3)
(2) x 5
40 M + 30 N = 470 --- (4)
(a)
(3) - (4)
(42 M + 30 N) - (40 M + 30 N) = 486 - 470
42 M - 40 M + 30 N - 30 N = 16
2 M = 16
1 M = 16 ÷ 2 = 8
(b)
Substitute M = 8 into (1).
7 M + 5 N = 81
7 x 8 + 5 N = 81
56 + 5 N = 81
5 N = 81 - 56 = 25
1 N = 25 ÷ 5 = 5
(c)
3 M + 4 N
= 3 x 8 + 4 x 5
= 24 + 20
= 44
Answer(s): (a) 8; (b) 5; (c) 44