7 J + 3 K = 68
8 J + 4 K = 80
Fill in the blanks.
- 1 J = _____
- 1 K = _____
- 4 J + 2 K = _____
(a)
7 J + 3 K = 68 --- (1)
8 J + 4 K = 80 --- (2)
Make K the same.
LCM of 3 and 4 = 12
(1) x 4
28 J + 12 K = 272 --- (3)
(2) x 3
24 J + 12 K = 240 --- (4)
(a)
(3) - (4)
(28 J + 12 K) - (24 J + 12 K) = 272 - 240
28 J - 24 J + 12 K - 12 K = 32
4 J = 32
1 J = 32 ÷ 4 = 8
(b)
Substitute J = 8 into (1).
7 J + 3 K = 68
7 x 8 + 3 K = 68
56 + 3 K = 68
3 K = 68 - 56 = 12
1 K = 12 ÷ 3 = 4
(c)
4 J + 2 K
= 4 x 8 + 2 x 4
= 32 + 8
= 40
Answer(s): (a) 8; (b) 4; (c) 40