7 C + 4 D = 54
8 C + 5 D = 63
Fill in the blanks.
- 1 C = _____
- 1 D = _____
- 5 C + 5 D = _____
(a)
7 C + 4 D = 54 --- (1)
8 C + 5 D = 63 --- (2)
Make D the same.
LCM of 4 and 5 = 20
(1) x 5
35 C + 20 D = 270 --- (3)
(2) x 4
32 C + 20 D = 252 --- (4)
(a)
(3) - (4)
(35 C + 20 D) - (32 C + 20 D) = 270 - 252
35 C - 32 C + 20 D - 20 D = 18
3 C = 18
1 C = 18 ÷ 3 = 6
(b)
Substitute C = 6 into (1).
7 C + 4 D = 54
7 x 6 + 4 D = 54
42 + 4 D = 54
4 D = 54 - 42 = 12
1 D = 12 ÷ 4 = 3
(c)
5 C + 5 D
= 5 x 6 + 5 x 3
= 30 + 15
= 45
Answer(s): (a) 6; (b) 3; (c) 45