7 Y + 5 Z = 76
8 Y + 6 Z = 88
Fill in the blanks.
- 1 Y = _____
- 1 Z = _____
- 3 Y + 5 Z = _____
(a)
7 Y + 5 Z = 76 --- (1)
8 Y + 6 Z = 88 --- (2)
Make Z the same.
LCM of 5 and 6 = 30
(1) x 6
42 Y + 30 Z = 456 --- (3)
(2) x 5
40 Y + 30 Z = 440 --- (4)
(a)
(3) - (4)
(42 Y + 30 Z) - (40 Y + 30 Z) = 456 - 440
42 Y - 40 Y + 30 Z - 30 Z = 16
2 Y = 16
1 Y = 16 ÷ 2 = 8
(b)
Substitute Y = 8 into (1).
7 Y + 5 Z = 76
7 x 8 + 5 Z = 76
56 + 5 Z = 76
5 Z = 76 - 56 = 20
1 Z = 20 ÷ 5 = 4
(c)
3 Y + 5 Z
= 3 x 8 + 5 x 4
= 24 + 20
= 44
Answer(s): (a) 8; (b) 4; (c) 44