Solve {l}{0.875-{(3/5-0.4)}x=3/16/0.3}{y=x}{z=y}{a=z}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { 0.875 - {(\frac{3}{5} - 0.4)} x = \frac{3}{16} / 0.3 }\\ { y = x }\\ { z = y }\\ { a = z }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for x, y, z, a, b

$$b=1.25$$

Solution Steps

Consider the first equation. Subtract 0.4 from \frac{3}{5} to get \frac{1}{5}.

$$0.875-\frac{1}{5}x=\frac{\frac{3}{16}}{0.3}$$

Express \frac{\frac{3}{16}}{0.3} as a single fraction.

$$0.875-\frac{1}{5}x=\frac{3}{16\times 0.3}$$

Multiply 16 and 0.3 to get 4.8.

$$0.875-\frac{1}{5}x=\frac{3}{4.8}$$

Expand \frac{3}{4.8} by multiplying both numerator and the denominator by 10.

$$0.875-\frac{1}{5}x=\frac{30}{48}$$

Reduce the fraction \frac{30}{48} to lowest terms by extracting and canceling out 6.

$$0.875-\frac{1}{5}x=\frac{5}{8}$$

Subtract 0.875 from both sides.

$$-\frac{1}{5}x=\frac{5}{8}-0.875$$

Subtract 0.875 from \frac{5}{8} to get -\frac{1}{4}.

$$-\frac{1}{5}x=-\frac{1}{4}$$

Multiply both sides by -5, the reciprocal of -\frac{1}{5}.

$$x=-\frac{1}{4}\left(-5\right)$$

Multiply -\frac{1}{4} and -5 to get \frac{5}{4}.

$$x=\frac{5}{4}$$

Consider the second equation. Insert the known values of variables into the equation.

$$y=\frac{5}{4}$$

Consider the third equation. Insert the known values of variables into the equation.

$$z=\frac{5}{4}$$

Consider the fourth equation. Insert the known values of variables into the equation.

$$a=\frac{5}{4}$$

Consider the fifth equation. Insert the known values of variables into the equation.

$$b=\frac{5}{4}$$

The system is now solved.

$$x=\frac{5}{4} y=\frac{5}{4} z=\frac{5}{4} a=\frac{5}{4} b=\frac{5}{4}$$