6 Q + 4 R = 24
7 Q + 5 R = 29
Fill in the blanks.
- 1 Q + 1 R = _____
- 1 Q = _____
- 1 R = _____
(a)
6 Q + 4 R = 24 --- (1)
7 Q + 5 R = 29 --- (2)
(2) - (1)
(7 Q + 5 R) - (6 Q + 4 R) = 29 - 24
7 Q - 6 Q + 5 R - 4 R = 5
1 Q + 1 R = 5 --- (3)
1 Q + 1 R = 5
(b)
Make R the same.
LCM of 1 and 4 = 4
(3) x 4
4 Q + 4 R = 20 --- (4)
(1) - (4)
(6 Q + 4 R) - (4 Q + 4 R) = 24 - 20
6 Q - 4 Q + 4 R - 4 R = 4
2 Q = 4
1 Q = 4 ÷ 2 = 2
(c)
Substitute 1 Q = 2 into (3).
1 Q + 1 R = 5
2 + 1 R = 5
1 R = 5 - 2 = 3
Answer(s): (a) 5; (b) 2; (c) 3