5 B + 2 C = 20
6 B + 3 C = 27
Fill in the blanks.
- 1 B + 1 C = _____
- 1 B = _____
- 1 C = _____
(a)
5 B + 2 C = 20 --- (1)
6 B + 3 C = 27 --- (2)
(2) - (1)
(6 B + 3 C) - (5 B + 2 C) = 27 - 20
6 B - 5 B + 3 C - 2 C = 7
1 B + 1 C = 7 --- (3)
1 B + 1 C = 7
(b)
Make C the same.
LCM of 1 and 2 = 2
(3) x 2
2 B + 2 C = 14 --- (4)
(1) - (4)
(5 B + 2 C) - (2 B + 2 C) = 20 - 14
5 B - 2 B + 2 C - 2 C = 6
3 B = 6
1 B = 6 ÷ 3 = 2
(c)
Substitute 1 B = 2 into (3).
1 B + 1 C = 7
2 + 1 C = 7
1 C = 7 - 2 = 5
Answer(s): (a) 7; (b) 2; (c) 5