7 L + 3 M = 51
8 L + 4 M = 60
Fill in the blanks.
- 1 L = _____
- 1 M = _____
- 4 L + 5 M = _____
(a)
7 L + 3 M = 51 --- (1)
8 L + 4 M = 60 --- (2)
Make M the same.
LCM of 3 and 4 = 12
(1) x 4
28 L + 12 M = 204 --- (3)
(2) x 3
24 L + 12 M = 180 --- (4)
(a)
(3) - (4)
(28 L + 12 M) - (24 L + 12 M) = 204 - 180
28 L - 24 L + 12 M - 12 M = 24
4 L = 24
1 L = 24 ÷ 4 = 6
(b)
Substitute L = 6 into (1).
7 L + 3 M = 51
7 x 6 + 3 M = 51
42 + 3 M = 51
3 M = 51 - 42 = 9
1 M = 9 ÷ 3 = 3
(c)
4 L + 5 M
= 4 x 6 + 5 x 3
= 24 + 15
= 39
Answer(s): (a) 6; (b) 3; (c) 39