The problem asks us to solve three equations for $x$, $y$, and $z$ respectively. a) $\frac{1.3 - 3x}{2} - \frac{1.8 - 8x}{1.2} = \frac{0.4 - 5x}{0.3}$ b) $1.2y - \frac{0.18y - 0.05}{0.5} = 0.4y + 8.9$ c) $\frac{0.02 - 2z}{0.02} - 7\frac{1}{2} = \frac{2(2 - 3z)}{0.01} - 2.5$

1. Problem Description

The problem asks us to solve three equations for $x$, $y$, and $z$ respectively.

a) $\frac{1.3 - 3x}{2} - \frac{1.8 - 8x}{1.2} = \frac{0.4 - 5x}{0.3}$

b) $1.2y - \frac{0.18y - 0.05}{0.5} = 0.4y + 8.9$

c) $\frac{0.02 - 2z}{0.02} - 7\frac{1}{2} = \frac{2(2 - 3z)}{0.01} - 2.5$

2. Solution Steps

a)

$\frac{1.3 - 3x}{2} - \frac{1.8 - 8x}{1.2} = \frac{0.4 - 5x}{0.3}$

Multiply both sides by 6 (LCM of 2, 1.2, 0.3):

$3(1.3 - 3x) - 5(1.8 - 8x) = 20(0.4 - 5x)$

$3.9 - 9x - 9 + 40x = 8 - 100x$

$31x - 5.1 = 8 - 100x$

$131x = 13.1$

$x = \frac{13.1}{131} = \frac{1}{10} = 0.1$

b)

$1.2y - \frac{0.18y - 0.05}{0.5} = 0.4y + 8.9$

Multiply both sides by 0.5:

$0.5(1.2y) - (0.18y - 0.05) = 0.5(0.4y) + 0.5(8.9)$

$0.6y - 0.18y + 0.05 = 0.2y + 4.45$

$0.42y + 0.05 = 0.2y + 4.45$

$0.22y = 4.4$

$y = \frac{4.4}{0.22} = \frac{440}{22} = 20$

c)

$\frac{0.02 - 2z}{0.02} - 7\frac{1}{2} = \frac{2(2 - 3z)}{0.01} - 2.5$

$\frac{0.02 - 2z}{0.02} - 7.5 = \frac{4 - 6z}{0.01} - 2.5$

Multiply by 0.02:

$(0.02 - 2z) - 0.02(7.5) = 2(4 - 6z) - 0.02(2.5)$

$0.02 - 2z - 0.15 = 8 - 12z - 0.05$

$-2z - 0.13 = 7.95 - 12z$

$10z = 8.08$

$z = \frac{8.08}{10} = 0.808$

3. Final Answer

a) $x = 0.1$

b) $y = 20$

c) $z = 0.808$