Solve {l}{5.0*10^4=0.01{(1+a)}*8.3*10^3}{b=340}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { 5.0 \cdot 10 ^ {4} = 0.01 {(1 + a)} \cdot 8.3 \cdot 10 ^ {3} }\\ { b = 340 }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

Solve for a, b, c

$$c=340$$

Solution Steps

Consider the first equation. Calculate 10 to the power of 4 and get 10000.

$$5\times 10000=0.01\left(1+a\right)\times 8.3\times 10^{3}$$

Multiply 5 and 10000 to get 50000.

$$50000=0.01\left(1+a\right)\times 8.3\times 10^{3}$$

Multiply 0.01 and 8.3 to get 0.083.

$$50000=0.083\left(1+a\right)\times 10^{3}$$

Calculate 10 to the power of 3 and get 1000.

$$50000=0.083\left(1+a\right)\times 1000$$

Multiply 0.083 and 1000 to get 83.

$$50000=83\left(1+a\right)$$

Use the distributive property to multiply 83 by 1+a.

$$50000=83+83a$$

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

$$83+83a=50000$$

Subtract 83 from both sides.

$$83a=50000-83$$

Subtract 83 from 50000 to get 49917.

$$83a=49917$$

Divide both sides by 83.

$$a=\frac{49917}{83}$$

The system is now solved.

$$a=\frac{49917}{83} b=340 c=340$$