7 Y + 4 Z = 91
8 Y + 5 Z = 107
Fill in the blanks.
- 1 Y = _____
- 1 Z = _____
- 4 Y + 3 Z = _____
(a)
7 Y + 4 Z = 91 --- (1)
8 Y + 5 Z = 107 --- (2)
Make Z the same.
LCM of 4 and 5 = 20
(1) x 5
35 Y + 20 Z = 455 --- (3)
(2) x 4
32 Y + 20 Z = 428 --- (4)
(a)
(3) - (4)
(35 Y + 20 Z) - (32 Y + 20 Z) = 455 - 428
35 Y - 32 Y + 20 Z - 20 Z = 27
3 Y = 27
1 Y = 27 ÷ 3 = 9
(b)
Substitute Y = 9 into (1).
7 Y + 4 Z = 91
7 x 9 + 4 Z = 91
63 + 4 Z = 91
4 Z = 91 - 63 = 28
1 Z = 28 ÷ 4 = 7
(c)
4 Y + 3 Z
= 4 x 9 + 3 x 7
= 36 + 21
= 57
Answer(s): (a) 9; (b) 7; (c) 57
