6 Q + 3 R = 60
7 Q + 4 R = 72
Fill in the blanks.
- 1 Q = _____
- 1 R = _____
- 5 Q + 2 R = _____
(a)
6 Q + 3 R = 60 --- (1)
7 Q + 4 R = 72 --- (2)
Make R the same.
LCM of 3 and 4 = 12
(1) x 4
24 Q + 12 R = 240 --- (3)
(2) x 3
21 Q + 12 R = 216 --- (4)
(a)
(3) - (4)
(24 Q + 12 R) - (21 Q + 12 R) = 240 - 216
24 Q - 21 Q + 12 R - 12 R = 24
3 Q = 24
1 Q = 24 ÷ 3 = 8
(b)
Substitute Q = 8 into (1).
6 Q + 3 R = 60
6 x 8 + 3 R = 60
48 + 3 R = 60
3 R = 60 - 48 = 12
1 R = 12 ÷ 3 = 4
(c)
5 Q + 2 R
= 5 x 8 + 2 x 4
= 40 + 8
= 48
Answer(s): (a) 8; (b) 4; (c) 48
