7 G + 5 H = 103
8 G + 6 H = 120
Fill in the blanks.
- 1 G = _____
- 1 H = _____
- 2 G + 2 H = _____
(a)
7 G + 5 H = 103 --- (1)
8 G + 6 H = 120 --- (2)
Make H the same.
LCM of 5 and 6 = 30
(1) x 6
42 G + 30 H = 618 --- (3)
(2) x 5
40 G + 30 H = 600 --- (4)
(a)
(3) - (4)
(42 G + 30 H) - (40 G + 30 H) = 618 - 600
42 G - 40 G + 30 H - 30 H = 18
2 G = 18
1 G = 18 ÷ 2 = 9
(b)
Substitute G = 9 into (1).
7 G + 5 H = 103
7 x 9 + 5 H = 103
63 + 5 H = 103
5 H = 103 - 63 = 40
1 H = 40 ÷ 5 = 8
(c)
2 G + 2 H
= 2 x 9 + 2 x 8
= 18 + 16
= 34
Answer(s): (a) 9; (b) 8; (c) 34
