5 J + 2 K = 25
6 J + 3 K = 33
Fill in the blanks.
- 1 J + 1 K = _____
- 1 J = _____
- 1 K = _____
(a)
5 J + 2 K = 25 --- (1)
6 J + 3 K = 33 --- (2)
(2) - (1)
(6 J + 3 K) - (5 J + 2 K) = 33 - 25
6 J - 5 J + 3 K - 2 K = 8
1 J + 1 K = 8 --- (3)
1 J + 1 K = 8
(b)
Make K the same.
LCM of 1 and 2 = 2
(3) x 2
2 J + 2 K = 16 --- (4)
(1) - (4)
(5 J + 2 K) - (2 J + 2 K) = 25 - 16
5 J - 2 J + 2 K - 2 K = 9
3 J = 9
1 J = 9 ÷ 3 = 3
(c)
Substitute 1 J = 3 into (3).
1 J + 1 K = 8
3 + 1 K = 8
1 K = 8 - 3 = 5
Answer(s): (a) 8; (b) 3; (c) 5
