7 M + 4 N = 53
8 M + 5 N = 64
Fill in the blanks.
- 1 M = _____
- 1 N = _____
- 2 M + 4 N = _____
(a)
7 M + 4 N = 53 --- (1)
8 M + 5 N = 64 --- (2)
Make N the same.
LCM of 4 and 5 = 20
(1) x 5
35 M + 20 N = 265 --- (3)
(2) x 4
32 M + 20 N = 256 --- (4)
(a)
(3) - (4)
(35 M + 20 N) - (32 M + 20 N) = 265 - 256
35 M - 32 M + 20 N - 20 N = 9
3 M = 9
1 M = 9 ÷ 3 = 3
(b)
Substitute M = 3 into (1).
7 M + 4 N = 53
7 x 3 + 4 N = 53
21 + 4 N = 53
4 N = 53 - 21 = 32
1 N = 32 ÷ 4 = 8
(c)
2 M + 4 N
= 2 x 3 + 4 x 8
= 6 + 32
= 38
Answer(s): (a) 3; (b) 8; (c) 38
