8 C + 3 D = 34
9 C + 4 D = 42
Fill in the blanks.
- 1 C = _____
- 1 D = _____
- 3 C + 5 D = _____
(a)
8 C + 3 D = 34 --- (1)
9 C + 4 D = 42 --- (2)
Make D the same.
LCM of 3 and 4 = 12
(1) x 4
32 C + 12 D = 136 --- (3)
(2) x 3
27 C + 12 D = 126 --- (4)
(a)
(3) - (4)
(32 C + 12 D) - (27 C + 12 D) = 136 - 126
32 C - 27 C + 12 D - 12 D = 10
5 C = 10
1 C = 10 ÷ 5 = 2
(b)
Substitute C = 2 into (1).
8 C + 3 D = 34
8 x 2 + 3 D = 34
16 + 3 D = 34
3 D = 34 - 16 = 18
1 D = 18 ÷ 3 = 6
(c)
3 C + 5 D
= 3 x 2 + 5 x 6
= 6 + 30
= 36
Answer(s): (a) 2; (b) 6; (c) 36