5 R + 2 S = 25
6 R + 3 S = 33
Fill in the blanks.
- 1 R + 1 S = _____
- 1 R = _____
- 1 S = _____
(a)
5 R + 2 S = 25 --- (1)
6 R + 3 S = 33 --- (2)
(2) - (1)
(6 R + 3 S) - (5 R + 2 S) = 33 - 25
6 R - 5 R + 3 S - 2 S = 8
1 R + 1 S = 8 --- (3)
1 R + 1 S = 8
(b)
Make S the same.
LCM of 1 and 2 = 2
(3) x 2
2 R + 2 S = 16 --- (4)
(1) - (4)
(5 R + 2 S) - (2 R + 2 S) = 25 - 16
5 R - 2 R + 2 S - 2 S = 9
3 R = 9
1 R = 9 ÷ 3 = 3
(c)
Substitute 1 R = 3 into (3).
1 R + 1 S = 8
3 + 1 S = 8
1 S = 8 - 3 = 5
Answer(s): (a) 8; (b) 3; (c) 5