Solve {l}{x+3y+z+w=48}{x=27.75*0.60}{z=3.10}{w=8+0.50*0.60}

$$\left\{ \begin{array} { l } { x + 3 y + z + w = 48 } \\ { x = 27.75 * 0.60 } \\ { z = 3.10 } \\ { w = 8 + 0.50 * 0.60 } \end{array} \right.$$

Solve for x, y, z, w

$$x=16.65$$

$$y=6.65$$

$$z=3.1$$

$$w=8.3$$

Solution Steps

Consider the second equation. Multiply 27.75 and 0.6 to get 16.65.

$$x=16.65$$

Consider the fourth equation. Multiply 0.5 and 0.6 to get 0.3.

$$w=8+0.3$$

Add 8 and 0.3 to get 8.3.

$$w=8.3$$

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

$$16.65+3y+3.1+8.3=48$$

Add 16.65 and 3.1 to get 19.75.

$$19.75+3y+8.3=48$$

Add 19.75 and 8.3 to get 28.05.

$$28.05+3y=48$$

Subtract 28.05 from both sides.

$$3y=48-28.05$$

Subtract 28.05 from 48 to get 19.95.

$$3y=19.95$$

Divide both sides by 3.

$$y=\frac{19.95}{3}$$

Expand \frac{19.95}{3} by multiplying both numerator and the denominator by 100.

$$y=\frac{1995}{300}$$

Reduce the fraction \frac{1995}{300} to lowest terms by extracting and canceling out 15.

$$y=\frac{133}{20}$$

The system is now solved.

$$x=16.65 y=\frac{133}{20} z=3.1 w=8.3$$