6 R + 3 S = 24
7 R + 4 S = 30
Fill in the blanks.
- 1 R + 1 S = _____
- 1 R = _____
- 1 S = _____
(a)
6 R + 3 S = 24 --- (1)
7 R + 4 S = 30 --- (2)
(2) - (1)
(7 R + 4 S) - (6 R + 3 S) = 30 - 24
7 R - 6 R + 4 S - 3 S = 6
1 R + 1 S = 6 --- (3)
1 R + 1 S = 6
(b)
Make S the same.
LCM of 1 and 3 = 3
(3) x 3
3 R + 3 S = 18 --- (4)
(1) - (4)
(6 R + 3 S) - (3 R + 3 S) = 24 - 18
6 R - 3 R + 3 S - 3 S = 6
3 R = 6
1 R = 6 ÷ 3 = 2
(c)
Substitute 1 R = 2 into (3).
1 R + 1 S = 6
2 + 1 S = 6
1 S = 6 - 2 = 4
Answer(s): (a) 6; (b) 2; (c) 4