Solve {l}{0.02a+0.0256+0.03c=1575}{a+b+c=60,000}{a+c=b}

$$\left. \begin{array} { l } { 0.02 a + 0.0256 + 0.03 c = 1575 } \\ { a + b + c = 60,000 } \\ { a + c = b } \end{array} \right.$$

Solve for a, c, b

$$a=-67497.44$$

$$c=97497.44$$

$$b=30000$$

Short Steps Using Substitution

Reorder the equations.

$$a+c=b a+b+c=60000 0.02a+0.0256+0.03c=1575$$

Solve a+c=b for b.

$$b=a+c$$

Substitute a+c for b in the equation a+b+c=60000.

$$a+a+c+c=60000$$

Solve the second equation for c and the third equation for a.

$$c=30000-a a=78748.72-1.5c$$

Substitute 30000-a for c in the equation a=78748.72-1.5c.

$$a=78748.72-1.5\left(30000-a\right)$$

Solve a=78748.72-1.5\left(30000-a\right) for a.

$$a=-67497.44$$

Substitute -67497.44 for a in the equation c=30000-a.

$$c=30000-\left(-67497.44\right)$$

Calculate c from c=30000-\left(-67497.44\right).

$$c=97497.44$$

Substitute 97497.44 for c and -67497.44 for a in the equation b=a+c.

$$b=-67497.44+97497.44$$

Calculate b from b=-67497.44+97497.44.

$$b=30000$$

The system is now solved.

$$a=-67497.44 c=97497.44 b=30000$$