6 K + 4 L = 68
7 K + 5 L = 82
Fill in the blanks.
- 1 K = _____
- 1 L = _____
- 3 K + 4 L = _____
(a)
6 K + 4 L = 68 --- (1)
7 K + 5 L = 82 --- (2)
Make L the same.
LCM of 4 and 5 = 20
(1) x 5
30 K + 20 L = 340 --- (3)
(2) x 4
28 K + 20 L = 328 --- (4)
(a)
(3) - (4)
(30 K + 20 L) - (28 K + 20 L) = 340 - 328
30 K - 28 K + 20 L - 20 L = 12
2 K = 12
1 K = 12 ÷ 2 = 6
(b)
Substitute K = 6 into (1).
6 K + 4 L = 68
6 x 6 + 4 L = 68
36 + 4 L = 68
4 L = 68 - 36 = 32
1 L = 32 ÷ 4 = 8
(c)
3 K + 4 L
= 3 x 6 + 4 x 8
= 18 + 32
= 50
Answer(s): (a) 6; (b) 8; (c) 50