Solve {l}{x+4.5y+z+w=48}{x=27.75*0.60}{z=6}{w=7+1.50*0.60}

$$\left\{ \begin{array} { l } { x + 4.5 y + z + w = 48 } \\ { x = 27.75 * 0.60 } \\ { z = 6 } \\ { w = 7 + 1.50 * 0.60 } \end{array} \right.$$

Solve for x, y, z, w

$$x=16.65$$

$$y = \frac{349}{90} = 3\frac{79}{90} \approx 3.877777778$$

$$z=6$$

$$w=7.9$$

Solution Steps

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

$$x=16.65$$

Consider the fourth equation. Multiply 1.5 and 0.6 to get 0.9.

$$w=7+0.9$$

Add 7 and 0.9 to get 7.9.

$$w=7.9$$

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

$$16.65+4.5y+6+7.9=48$$

Add 16.65 and 6 to get 22.65.

$$22.65+4.5y+7.9=48$$

Add 22.65 and 7.9 to get 30.55.

$$30.55+4.5y=48$$

Subtract 30.55 from both sides.

$$4.5y=48-30.55$$

Subtract 30.55 from 48 to get 17.45.

$$4.5y=17.45$$

Divide both sides by 4.5.

$$y=\frac{17.45}{4.5}$$

Expand \frac{17.45}{4.5} by multiplying both numerator and the denominator by 100.

$$y=\frac{1745}{450}$$

Reduce the fraction \frac{1745}{450} to lowest terms by extracting and canceling out 5.

$$y=\frac{349}{90}$$

The system is now solved.

$$x=16.65 y=\frac{349}{90} z=6 w=7.9$$