7 U + 4 V = 50
8 U + 5 V = 58
Fill in the blanks.
- 1 U = _____
- 1 V = _____
- 2 U + 5 V = _____
(a)
7 U + 4 V = 50 --- (1)
8 U + 5 V = 58 --- (2)
Make V the same.
LCM of 4 and 5 = 20
(1) x 5
35 U + 20 V = 250 --- (3)
(2) x 4
32 U + 20 V = 232 --- (4)
(a)
(3) - (4)
(35 U + 20 V) - (32 U + 20 V) = 250 - 232
35 U - 32 U + 20 V - 20 V = 18
3 U = 18
1 U = 18 ÷ 3 = 6
(b)
Substitute U = 6 into (1).
7 U + 4 V = 50
7 x 6 + 4 V = 50
42 + 4 V = 50
4 V = 50 - 42 = 8
1 V = 8 ÷ 4 = 2
(c)
2 U + 5 V
= 2 x 6 + 5 x 2
= 12 + 10
= 22
Answer(s): (a) 6; (b) 2; (c) 22