5 C + 3 D = 41
6 C + 4 D = 52
Fill in the blanks.
- 1 C = _____
- 1 D = _____
- 2 C + 2 D = _____
(a)
5 C + 3 D = 41 --- (1)
6 C + 4 D = 52 --- (2)
Make D the same.
LCM of 3 and 4 = 12
(1) x 4
20 C + 12 D = 164 --- (3)
(2) x 3
18 C + 12 D = 156 --- (4)
(a)
(3) - (4)
(20 C + 12 D) - (18 C + 12 D) = 164 - 156
20 C - 18 C + 12 D - 12 D = 8
2 C = 8
1 C = 8 ÷ 2 = 4
(b)
Substitute C = 4 into (1).
5 C + 3 D = 41
5 x 4 + 3 D = 41
20 + 3 D = 41
3 D = 41 - 20 = 21
1 D = 21 ÷ 3 = 7
(c)
2 C + 2 D
= 2 x 4 + 2 x 7
= 8 + 14
= 22
Answer(s): (a) 4; (b) 7; (c) 22