Page 50 - Algebra

2. Let the first amount be x Second amount be y 0.12x + 0.15y = 225.6 0.15x + 0.12y = 255
or
0.04x + 0.05y = 75.2 0.05x + 0.04y = 85
4x + 5y = 7520............(1) 5x + 4y = 8500............(2)
Multiply (1) by 5 and (2) by 4 20x + 25y = 37600
20x + 16y = 34000
Subtract the two equations. 9y = 3600
y = 400
0.05x + 0.04y = 85
0.05x + 0.04(400) = 85 0.05x + 16 = 85
0.05x = 69
x = 1380
3.
Let the number of rows be x and the number of workers in each row be y.
Number of workers in the factory = xy
(x – 3)(y + 4) = xy (x + 2) (y – 2) =xy
xy + 4x – 3y – 12 = xy
xy + 2y – 2x – 4 = xy
4x – 3y = 12
– 2x + 2y = 4
4x – 3y = 12
– 4x + 4y = 8
Add the two
y = 20
x = 18
– 2x + 2y = 4
– 2x + 2(20) = 4
– 2x = –36
Number of workers = xy = 18 × 20 = 360
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Algebra I & II