Solve {l}{7:2=21:x}{3:z=1.5:4}{m*3=1/21/4}

$$\left. \begin{array} { l } { 7 : 2 = 21 : x } \\ { 3 : z = 1.5 : 4 } \\ { m \cdot 3 = \frac { 1 } { 2 } \frac { 1 } { 4 } } \end{array} \right.$$

Solve for x, z, m

$$x=6$$

$$z=8$$

$$m=\frac{1}{24}\approx 0.041666667$$

Solution Steps

Consider the first equation. Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of 2,x.

$$7x=2\times 21$$

Multiply 2 and 21 to get 42.

$$7x=42$$

Divide both sides by 7.

$$x=\frac{42}{7}$$

Divide 42 by 7 to get 6.

$$x=6$$

Consider the second equation. Variable z cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4z, the least common multiple of z,4.

$$4\times 3=z\times 1.5$$

Multiply 4 and 3 to get 12.

$$12=z\times 1.5$$

Swap sides so that all variable terms are on the left hand side.

$$z\times 1.5=12$$

Divide both sides by 1.5.

$$z=\frac{12}{1.5}$$

Expand \frac{12}{1.5} by multiplying both numerator and the denominator by 10.

$$z=\frac{120}{15}$$

Divide 120 by 15 to get 8.

$$z=8$$

Consider the third equation. Multiply \frac{1}{2} and \frac{1}{4} to get \frac{1}{8}.

$$m\times 3=\frac{1}{8}$$

Divide both sides by 3.

$$m=\frac{\frac{1}{8}}{3}$$

Express \frac{\frac{1}{8}}{3} as a single fraction.

$$m=\frac{1}{8\times 3}$$

Multiply 8 and 3 to get 24.

$$m=\frac{1}{24}$$

The system is now solved.

$$x=6 z=8 m=\frac{1}{24}$$