Solve {l}{U=3K/4}{K+3k/4=35}{7k/4=35}

$$\left. \begin{array} { l } { U = \frac { 3 K } { 4 } } \\ { K + \frac { 3 k } { 4 } = 35 } \\ { \frac { 7 k } { 4 } = 35 } \end{array} \right.$$

Solve for U, K, k

$$U=15$$

$$K=20$$

$$k=20$$

Solution Steps

Consider the third equation. Multiply both sides by 4.

$$7k=35\times 4$$

Multiply 35 and 4 to get 140.

$$7k=140$$

Divide both sides by 7.

$$k=\frac{140}{7}$$

Divide 140 by 7 to get 20.

$$k=20$$

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

$$K+\frac{3\times 20}{4}=35$$

Multiply both sides of the equation by 4.

$$4K+3\times 20=140$$

Multiply 3 and 20 to get 60.

$$4K+60=140$$

Subtract 60 from both sides.

$$4K=140-60$$

Subtract 60 from 140 to get 80.

$$4K=80$$

Divide both sides by 4.

$$K=\frac{80}{4}$$

Divide 80 by 4 to get 20.

$$K=20$$

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

$$U=\frac{3\times 20}{4}$$

Multiply 3 and 20 to get 60.

$$U=\frac{60}{4}$$

Divide 60 by 4 to get 15.

$$U=15$$

The system is now solved.

$$U=15 K=20 k=20$$