6 L + 3 M = 75
7 L + 4 M = 92
Fill in the blanks.
- 1 L = _____
- 1 M = _____
- 2 L + 3 M = _____
(a)
6 L + 3 M = 75 --- (1)
7 L + 4 M = 92 --- (2)
Make M the same.
LCM of 3 and 4 = 12
(1) x 4
24 L + 12 M = 300 --- (3)
(2) x 3
21 L + 12 M = 276 --- (4)
(a)
(3) - (4)
(24 L + 12 M) - (21 L + 12 M) = 300 - 276
24 L - 21 L + 12 M - 12 M = 24
3 L = 24
1 L = 24 ÷ 3 = 8
(b)
Substitute L = 8 into (1).
6 L + 3 M = 75
6 x 8 + 3 M = 75
48 + 3 M = 75
3 M = 75 - 48 = 27
1 M = 27 ÷ 3 = 9
(c)
2 L + 3 M
= 2 x 8 + 3 x 9
= 16 + 27
= 43
Answer(s): (a) 8; (b) 9; (c) 43