7 F + 3 G = 75
8 F + 4 G = 88
Fill in the blanks.
- 1 F = _____
- 1 G = _____
- 4 F + 3 G = _____
(a)
7 F + 3 G = 75 --- (1)
8 F + 4 G = 88 --- (2)
Make G the same.
LCM of 3 and 4 = 12
(1) x 4
28 F + 12 G = 300 --- (3)
(2) x 3
24 F + 12 G = 264 --- (4)
(a)
(3) - (4)
(28 F + 12 G) - (24 F + 12 G) = 300 - 264
28 F - 24 F + 12 G - 12 G = 36
4 F = 36
1 F = 36 ÷ 4 = 9
(b)
Substitute F = 9 into (1).
7 F + 3 G = 75
7 x 9 + 3 G = 75
63 + 3 G = 75
3 G = 75 - 63 = 12
1 G = 12 ÷ 3 = 4
(c)
4 F + 3 G
= 4 x 9 + 3 x 4
= 36 + 12
= 48
Answer(s): (a) 9; (b) 4; (c) 48
