8 K + 4 L = 88
9 K + 5 L = 101
Fill in the blanks.
- 1 K = _____
- 1 L = _____
- 2 K + 2 L = _____
(a)
8 K + 4 L = 88 --- (1)
9 K + 5 L = 101 --- (2)
Make L the same.
LCM of 4 and 5 = 20
(1) x 5
40 K + 20 L = 440 --- (3)
(2) x 4
36 K + 20 L = 404 --- (4)
(a)
(3) - (4)
(40 K + 20 L) - (36 K + 20 L) = 440 - 404
40 K - 36 K + 20 L - 20 L = 36
4 K = 36
1 K = 36 ÷ 4 = 9
(b)
Substitute K = 9 into (1).
8 K + 4 L = 88
8 x 9 + 4 L = 88
72 + 4 L = 88
4 L = 88 - 72 = 16
1 L = 16 ÷ 4 = 4
(c)
2 K + 2 L
= 2 x 9 + 2 x 4
= 18 + 8
= 26
Answer(s): (a) 9; (b) 4; (c) 26