6 B + 3 C = 30
7 B + 4 C = 37
Fill in the blanks.
- 1 B + 1 C = _____
- 1 B = _____
- 1 C = _____
(a)
6 B + 3 C = 30 --- (1)
7 B + 4 C = 37 --- (2)
(2) - (1)
(7 B + 4 C) - (6 B + 3 C) = 37 - 30
7 B - 6 B + 4 C - 3 C = 7
1 B + 1 C = 7 --- (3)
1 B + 1 C = 7
(b)
Make C the same.
LCM of 1 and 3 = 3
(3) x 3
3 B + 3 C = 21 --- (4)
(1) - (4)
(6 B + 3 C) - (3 B + 3 C) = 30 - 21
6 B - 3 B + 3 C - 3 C = 9
3 B = 9
1 B = 9 ÷ 3 = 3
(c)
Substitute 1 B = 3 into (3).
1 B + 1 C = 7
3 + 1 C = 7
1 C = 7 - 3 = 4
Answer(s): (a) 7; (b) 3; (c) 4