8 K + 4 L = 36
9 K + 5 L = 43
Fill in the blanks.
- 1 K = _____
- 1 L = _____
- 4 K + 4 L = _____
(a)
8 K + 4 L = 36 --- (1)
9 K + 5 L = 43 --- (2)
Make L the same.
LCM of 4 and 5 = 20
(1) x 5
40 K + 20 L = 180 --- (3)
(2) x 4
36 K + 20 L = 172 --- (4)
(a)
(3) - (4)
(40 K + 20 L) - (36 K + 20 L) = 180 - 172
40 K - 36 K + 20 L - 20 L = 8
4 K = 8
1 K = 8 ÷ 4 = 2
(b)
Substitute K = 2 into (1).
8 K + 4 L = 36
8 x 2 + 4 L = 36
16 + 4 L = 36
4 L = 36 - 16 = 20
1 L = 20 ÷ 4 = 5
(c)
4 K + 4 L
= 4 x 2 + 4 x 5
= 8 + 20
= 28
Answer(s): (a) 2; (b) 5; (c) 28
