6 C + 3 D = 45
7 C + 4 D = 54
Fill in the blanks.
- 1 C = _____
- 1 D = _____
- 3 C + 4 D = _____
(a)
6 C + 3 D = 45 --- (1)
7 C + 4 D = 54 --- (2)
Make D the same.
LCM of 3 and 4 = 12
(1) x 4
24 C + 12 D = 180 --- (3)
(2) x 3
21 C + 12 D = 162 --- (4)
(a)
(3) - (4)
(24 C + 12 D) - (21 C + 12 D) = 180 - 162
24 C - 21 C + 12 D - 12 D = 18
3 C = 18
1 C = 18 ÷ 3 = 6
(b)
Substitute C = 6 into (1).
6 C + 3 D = 45
6 x 6 + 3 D = 45
36 + 3 D = 45
3 D = 45 - 36 = 9
1 D = 9 ÷ 3 = 3
(c)
3 C + 4 D
= 3 x 6 + 4 x 3
= 18 + 12
= 30
Answer(s): (a) 6; (b) 3; (c) 30