7 G + 5 H = 74
8 G + 6 H = 86
Fill in the blanks.
- 1 G = _____
- 1 H = _____
- 4 G + 4 H = _____
(a)
7 G + 5 H = 74 --- (1)
8 G + 6 H = 86 --- (2)
Make H the same.
LCM of 5 and 6 = 30
(1) x 6
42 G + 30 H = 444 --- (3)
(2) x 5
40 G + 30 H = 430 --- (4)
(a)
(3) - (4)
(42 G + 30 H) - (40 G + 30 H) = 444 - 430
42 G - 40 G + 30 H - 30 H = 14
2 G = 14
1 G = 14 ÷ 2 = 7
(b)
Substitute G = 7 into (1).
7 G + 5 H = 74
7 x 7 + 5 H = 74
49 + 5 H = 74
5 H = 74 - 49 = 25
1 H = 25 ÷ 5 = 5
(c)
4 G + 4 H
= 4 x 7 + 4 x 5
= 28 + 20
= 48
Answer(s): (a) 7; (b) 5; (c) 48