6 R + 3 S = 78
7 R + 4 S = 95
Fill in the blanks.
- 1 R = _____
- 1 S = _____
- 3 R + 5 S = _____
(a)
6 R + 3 S = 78 --- (1)
7 R + 4 S = 95 --- (2)
Make S the same.
LCM of 3 and 4 = 12
(1) x 4
24 R + 12 S = 312 --- (3)
(2) x 3
21 R + 12 S = 285 --- (4)
(a)
(3) - (4)
(24 R + 12 S) - (21 R + 12 S) = 312 - 285
24 R - 21 R + 12 S - 12 S = 27
3 R = 27
1 R = 27 ÷ 3 = 9
(b)
Substitute R = 9 into (1).
6 R + 3 S = 78
6 x 9 + 3 S = 78
54 + 3 S = 78
3 S = 78 - 54 = 24
1 S = 24 ÷ 3 = 8
(c)
3 R + 5 S
= 3 x 9 + 5 x 8
= 27 + 40
= 67
Answer(s): (a) 9; (b) 8; (c) 67
