6 C + 3 D = 30
7 C + 4 D = 37
Fill in the blanks.
- 1 C + 1 D = _____
- 1 C = _____
- 1 D = _____
(a)
6 C + 3 D = 30 --- (1)
7 C + 4 D = 37 --- (2)
(2) - (1)
(7 C + 4 D) - (6 C + 3 D) = 37 - 30
7 C - 6 C + 4 D - 3 D = 7
1 C + 1 D = 7 --- (3)
1 C + 1 D = 7
(b)
Make D the same.
LCM of 1 and 3 = 3
(3) x 3
3 C + 3 D = 21 --- (4)
(1) - (4)
(6 C + 3 D) - (3 C + 3 D) = 30 - 21
6 C - 3 C + 3 D - 3 D = 9
3 C = 9
1 C = 9 ÷ 3 = 3
(c)
Substitute 1 C = 3 into (3).
1 C + 1 D = 7
3 + 1 D = 7
1 D = 7 - 3 = 4
Answer(s): (a) 7; (b) 3; (c) 4