7 D + 4 E = 53
8 D + 5 E = 64
Fill in the blanks.
- 1 D = _____
- 1 E = _____
- 4 D + 5 E = _____
(a)
7 D + 4 E = 53 --- (1)
8 D + 5 E = 64 --- (2)
Make E the same.
LCM of 4 and 5 = 20
(1) x 5
35 D + 20 E = 265 --- (3)
(2) x 4
32 D + 20 E = 256 --- (4)
(a)
(3) - (4)
(35 D + 20 E) - (32 D + 20 E) = 265 - 256
35 D - 32 D + 20 E - 20 E = 9
3 D = 9
1 D = 9 ÷ 3 = 3
(b)
Substitute D = 3 into (1).
7 D + 4 E = 53
7 x 3 + 4 E = 53
21 + 4 E = 53
4 E = 53 - 21 = 32
1 E = 32 ÷ 4 = 8
(c)
4 D + 5 E
= 4 x 3 + 5 x 8
= 12 + 40
= 52
Answer(s): (a) 3; (b) 8; (c) 52
