8 G + 3 H = 87
9 G + 4 H = 101
Fill in the blanks.
- 1 G = _____
- 1 H = _____
- 4 G + 3 H = _____
(a)
8 G + 3 H = 87 --- (1)
9 G + 4 H = 101 --- (2)
Make H the same.
LCM of 3 and 4 = 12
(1) x 4
32 G + 12 H = 348 --- (3)
(2) x 3
27 G + 12 H = 303 --- (4)
(a)
(3) - (4)
(32 G + 12 H) - (27 G + 12 H) = 348 - 303
32 G - 27 G + 12 H - 12 H = 45
5 G = 45
1 G = 45 ÷ 5 = 9
(b)
Substitute G = 9 into (1).
8 G + 3 H = 87
8 x 9 + 3 H = 87
72 + 3 H = 87
3 H = 87 - 72 = 15
1 H = 15 ÷ 3 = 5
(c)
4 G + 3 H
= 4 x 9 + 3 x 5
= 36 + 15
= 51
Answer(s): (a) 9; (b) 5; (c) 51
