6 U + 4 V = 54
7 U + 5 V = 64
Fill in the blanks.
- 1 U = _____
- 1 V = _____
- 5 U + 4 V = _____
(a)
6 U + 4 V = 54 --- (1)
7 U + 5 V = 64 --- (2)
Make V the same.
LCM of 4 and 5 = 20
(1) x 5
30 U + 20 V = 270 --- (3)
(2) x 4
28 U + 20 V = 256 --- (4)
(a)
(3) - (4)
(30 U + 20 V) - (28 U + 20 V) = 270 - 256
30 U - 28 U + 20 V - 20 V = 14
2 U = 14
1 U = 14 ÷ 2 = 7
(b)
Substitute U = 7 into (1).
6 U + 4 V = 54
6 x 7 + 4 V = 54
42 + 4 V = 54
4 V = 54 - 42 = 12
1 V = 12 ÷ 4 = 3
(c)
5 U + 4 V
= 5 x 7 + 4 x 3
= 35 + 12
= 47
Answer(s): (a) 7; (b) 3; (c) 47
