5 C + 2 D = 24
6 C + 3 D = 30
Fill in the blanks.
- 1 C + 1 D = _____
- 1 C = _____
- 1 D = _____
(a)
5 C + 2 D = 24 --- (1)
6 C + 3 D = 30 --- (2)
(2) - (1)
(6 C + 3 D) - (5 C + 2 D) = 30 - 24
6 C - 5 C + 3 D - 2 D = 6
1 C + 1 D = 6 --- (3)
1 C + 1 D = 6
(b)
Make D the same.
LCM of 1 and 2 = 2
(3) x 2
2 C + 2 D = 12 --- (4)
(1) - (4)
(5 C + 2 D) - (2 C + 2 D) = 24 - 12
5 C - 2 C + 2 D - 2 D = 12
3 C = 12
1 C = 12 ÷ 3 = 4
(c)
Substitute 1 C = 4 into (3).
1 C + 1 D = 6
4 + 1 D = 6
1 D = 6 - 4 = 2
Answer(s): (a) 6; (b) 4; (c) 2