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