5 J + 3 K = 19
6 J + 4 K = 24
Fill in the blanks.
- 1 J + 1 K = _____
- 1 J = _____
- 1 K = _____
(a)
5 J + 3 K = 19 --- (1)
6 J + 4 K = 24 --- (2)
(2) - (1)
(6 J + 4 K) - (5 J + 3 K) = 24 - 19
6 J - 5 J + 4 K - 3 K = 5
1 J + 1 K = 5 --- (3)
1 J + 1 K = 5
(b)
Make K the same.
LCM of 1 and 3 = 3
(3) x 3
3 J + 3 K = 15 --- (4)
(1) - (4)
(5 J + 3 K) - (3 J + 3 K) = 19 - 15
5 J - 3 J + 3 K - 3 K = 4
2 J = 4
1 J = 4 ÷ 2 = 2
(c)
Substitute 1 J = 2 into (3).
1 J + 1 K = 5
2 + 1 K = 5
1 K = 5 - 2 = 3
Answer(s): (a) 5; (b) 2; (c) 3
