8 M + 3 N = 75
9 M + 4 N = 90
Fill in the blanks.
- 1 M = _____
- 1 N = _____
- 4 M + 3 N = _____
(a)
8 M + 3 N = 75 --- (1)
9 M + 4 N = 90 --- (2)
Make N the same.
LCM of 3 and 4 = 12
(1) x 4
32 M + 12 N = 300 --- (3)
(2) x 3
27 M + 12 N = 270 --- (4)
(a)
(3) - (4)
(32 M + 12 N) - (27 M + 12 N) = 300 - 270
32 M - 27 M + 12 N - 12 N = 30
5 M = 30
1 M = 30 ÷ 5 = 6
(b)
Substitute M = 6 into (1).
8 M + 3 N = 75
8 x 6 + 3 N = 75
48 + 3 N = 75
3 N = 75 - 48 = 27
1 N = 27 ÷ 3 = 9
(c)
4 M + 3 N
= 4 x 6 + 3 x 9
= 24 + 27
= 51
Answer(s): (a) 6; (b) 9; (c) 51
