Solve {l}{B/2+{(frac{1*{(4)}+1}{4})}=8}{a=B}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { \frac{B}{2} + {(\frac{1 \cdot {(4)} + 1}{4})} = 8 }\\ { a = B }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for B, a, b

$$b = \frac{27}{2} = 13\frac{1}{2} = 13.5$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2B+1\times 4+1=32$$

Multiply 1 and 4 to get 4.

$$2B+4+1=32$$

Add 4 and 1 to get 5.

$$2B+5=32$$

Subtract 5 from both sides.

$$2B=32-5$$

Subtract 5 from 32 to get 27.

$$2B=27$$

Divide both sides by 2.

$$B=\frac{27}{2}$$

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

$$a=\frac{27}{2}$$

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

$$b=\frac{27}{2}$$

The system is now solved.

$$B=\frac{27}{2} a=\frac{27}{2} b=\frac{27}{2}$$