7 Q + 5 R = 61
8 Q + 6 R = 72
Fill in the blanks.
- 1 Q = _____
- 1 R = _____
- 2 Q + 3 R = _____
(a)
7 Q + 5 R = 61 --- (1)
8 Q + 6 R = 72 --- (2)
Make R the same.
LCM of 5 and 6 = 30
(1) x 6
42 Q + 30 R = 366 --- (3)
(2) x 5
40 Q + 30 R = 360 --- (4)
(a)
(3) - (4)
(42 Q + 30 R) - (40 Q + 30 R) = 366 - 360
42 Q - 40 Q + 30 R - 30 R = 6
2 Q = 6
1 Q = 6 ÷ 2 = 3
(b)
Substitute Q = 3 into (1).
7 Q + 5 R = 61
7 x 3 + 5 R = 61
21 + 5 R = 61
5 R = 61 - 21 = 40
1 R = 40 ÷ 5 = 8
(c)
2 Q + 3 R
= 2 x 3 + 3 x 8
= 6 + 24
= 30
Answer(s): (a) 3; (b) 8; (c) 30
