8 T + 6 U = 94
9 T + 7 U = 107
Fill in the blanks.
- 1 T = _____
- 1 U = _____
- 5 T + 4 U = _____
(a)
8 T + 6 U = 94 --- (1)
9 T + 7 U = 107 --- (2)
Make U the same.
LCM of 6 and 7 = 42
(1) x 7
56 T + 42 U = 658 --- (3)
(2) x 6
54 T + 42 U = 642 --- (4)
(a)
(3) - (4)
(56 T + 42 U) - (54 T + 42 U) = 658 - 642
56 T - 54 T + 42 U - 42 U = 16
2 T = 16
1 T = 16 ÷ 2 = 8
(b)
Substitute T = 8 into (1).
8 T + 6 U = 94
8 x 8 + 6 U = 94
64 + 6 U = 94
6 U = 94 - 64 = 30
1 U = 30 ÷ 6 = 5
(c)
5 T + 4 U
= 5 x 8 + 4 x 5
= 40 + 20
= 60
Answer(s): (a) 8; (b) 5; (c) 60