6 F + 3 G = 36
7 F + 4 G = 43
Fill in the blanks.
- 1 F = _____
- 1 G = _____
- 2 F + 2 G = _____
(a)
6 F + 3 G = 36 --- (1)
7 F + 4 G = 43 --- (2)
Make G the same.
LCM of 3 and 4 = 12
(1) x 4
24 F + 12 G = 144 --- (3)
(2) x 3
21 F + 12 G = 129 --- (4)
(a)
(3) - (4)
(24 F + 12 G) - (21 F + 12 G) = 144 - 129
24 F - 21 F + 12 G - 12 G = 15
3 F = 15
1 F = 15 ÷ 3 = 5
(b)
Substitute F = 5 into (1).
6 F + 3 G = 36
6 x 5 + 3 G = 36
30 + 3 G = 36
3 G = 36 - 30 = 6
1 G = 6 ÷ 3 = 2
(c)
2 F + 2 G
= 2 x 5 + 2 x 2
= 10 + 4
= 14
Answer(s): (a) 5; (b) 2; (c) 14
