Solve {l}{-75000+41000/1.15}{+44000/1.15^2}{+44000/1.15^3}

$$\left. \begin{array} { l } { - 75000 + \frac { 41000 } { 1.15 } } \\ { + \frac { 44000 } { 1.15 ^ { 2 } } } \\ { + \frac { 44000 } { 1.15 ^ { 3 } } } \end{array} \right.$$

Evaluate

$$\frac{278055000}{12167}\approx 22853.20950111$$

Solution Steps

Expand \frac{41000}{1.15} by multiplying both numerator and the denominator by 100.

$$-75000+\frac{4100000}{115}+\frac{44000}{1.15^{2}}+\frac{44000}{1.15^{3}}$$

Reduce the fraction \frac{4100000}{115} to lowest terms by extracting and canceling out 5.

$$-75000+\frac{820000}{23}+\frac{44000}{1.15^{2}}+\frac{44000}{1.15^{3}}$$

Convert -75000 to fraction -\frac{1725000}{23}.

$$-\frac{1725000}{23}+\frac{820000}{23}+\frac{44000}{1.15^{2}}+\frac{44000}{1.15^{3}}$$

Since -\frac{1725000}{23} and \frac{820000}{23} have the same denominator, add them by adding their numerators.

$$\frac{-1725000+820000}{23}+\frac{44000}{1.15^{2}}+\frac{44000}{1.15^{3}}$$

Add -1725000 and 820000 to get -905000.

$$-\frac{905000}{23}+\frac{44000}{1.15^{2}}+\frac{44000}{1.15^{3}}$$

Calculate 1.15 to the power of 2 and get 1.3225.

$$-\frac{905000}{23}+\frac{44000}{1.3225}+\frac{44000}{1.15^{3}}$$

Expand \frac{44000}{1.3225} by multiplying both numerator and the denominator by 10000.

$$-\frac{905000}{23}+\frac{440000000}{13225}+\frac{44000}{1.15^{3}}$$

Reduce the fraction \frac{440000000}{13225} to lowest terms by extracting and canceling out 25.

$$-\frac{905000}{23}+\frac{17600000}{529}+\frac{44000}{1.15^{3}}$$

Least common multiple of 23 and 529 is 529. Convert -\frac{905000}{23} and \frac{17600000}{529} to fractions with denominator 529.

$$-\frac{20815000}{529}+\frac{17600000}{529}+\frac{44000}{1.15^{3}}$$

Since -\frac{20815000}{529} and \frac{17600000}{529} have the same denominator, add them by adding their numerators.

$$\frac{-20815000+17600000}{529}+\frac{44000}{1.15^{3}}$$

Add -20815000 and 17600000 to get -3215000.

$$-\frac{3215000}{529}+\frac{44000}{1.15^{3}}$$

Calculate 1.15 to the power of 3 and get 1.520875.

$$-\frac{3215000}{529}+\frac{44000}{1.520875}$$

Expand \frac{44000}{1.520875} by multiplying both numerator and the denominator by 1000000.

$$-\frac{3215000}{529}+\frac{44000000000}{1520875}$$

Reduce the fraction \frac{44000000000}{1520875} to lowest terms by extracting and canceling out 125.

$$-\frac{3215000}{529}+\frac{352000000}{12167}$$

Least common multiple of 529 and 12167 is 12167. Convert -\frac{3215000}{529} and \frac{352000000}{12167} to fractions with denominator 12167.

$$-\frac{73945000}{12167}+\frac{352000000}{12167}$$

Since -\frac{73945000}{12167} and \frac{352000000}{12167} have the same denominator, add them by adding their numerators.

$$\frac{-73945000+352000000}{12167}$$

Add -73945000 and 352000000 to get 278055000.

$$\frac{278055000}{12167}$$

Factor

$$\frac{37 \cdot 167 \cdot 2 ^ {3} \cdot 3 ^ {2} \cdot 5 ^ {4}}{23 ^ {3}} = 22853\frac{2549}{12167} = 22853.20950110956$$