8 K + 3 L = 90
9 K + 4 L = 105
Fill in the blanks.
- 1 K = _____
- 1 L = _____
- 2 K + 5 L = _____
(a)
8 K + 3 L = 90 --- (1)
9 K + 4 L = 105 --- (2)
Make L the same.
LCM of 3 and 4 = 12
(1) x 4
32 K + 12 L = 360 --- (3)
(2) x 3
27 K + 12 L = 315 --- (4)
(a)
(3) - (4)
(32 K + 12 L) - (27 K + 12 L) = 360 - 315
32 K - 27 K + 12 L - 12 L = 45
5 K = 45
1 K = 45 ÷ 5 = 9
(b)
Substitute K = 9 into (1).
8 K + 3 L = 90
8 x 9 + 3 L = 90
72 + 3 L = 90
3 L = 90 - 72 = 18
1 L = 18 ÷ 3 = 6
(c)
2 K + 5 L
= 2 x 9 + 5 x 6
= 18 + 30
= 48
Answer(s): (a) 9; (b) 6; (c) 48