7 L + 4 M = 71
8 L + 5 M = 85
Fill in the blanks.
- 1 L = _____
- 1 M = _____
- 3 L + 2 M = _____
(a)
7 L + 4 M = 71 --- (1)
8 L + 5 M = 85 --- (2)
Make M the same.
LCM of 4 and 5 = 20
(1) x 5
35 L + 20 M = 355 --- (3)
(2) x 4
32 L + 20 M = 340 --- (4)
(a)
(3) - (4)
(35 L + 20 M) - (32 L + 20 M) = 355 - 340
35 L - 32 L + 20 M - 20 M = 15
3 L = 15
1 L = 15 ÷ 3 = 5
(b)
Substitute L = 5 into (1).
7 L + 4 M = 71
7 x 5 + 4 M = 71
35 + 4 M = 71
4 M = 71 - 35 = 36
1 M = 36 ÷ 4 = 9
(c)
3 L + 2 M
= 3 x 5 + 2 x 9
= 15 + 18
= 33
Answer(s): (a) 5; (b) 9; (c) 33