6 K + 3 L = 54
7 K + 4 L = 64
Fill in the blanks.
- 1 K = _____
- 1 L = _____
- 5 K + 3 L = _____
(a)
6 K + 3 L = 54 --- (1)
7 K + 4 L = 64 --- (2)
Make L the same.
LCM of 3 and 4 = 12
(1) x 4
24 K + 12 L = 216 --- (3)
(2) x 3
21 K + 12 L = 192 --- (4)
(a)
(3) - (4)
(24 K + 12 L) - (21 K + 12 L) = 216 - 192
24 K - 21 K + 12 L - 12 L = 24
3 K = 24
1 K = 24 ÷ 3 = 8
(b)
Substitute K = 8 into (1).
6 K + 3 L = 54
6 x 8 + 3 L = 54
48 + 3 L = 54
3 L = 54 - 48 = 6
1 L = 6 ÷ 3 = 2
(c)
5 K + 3 L
= 5 x 8 + 3 x 2
= 40 + 6
= 46
Answer(s): (a) 8; (b) 2; (c) 46