Solve x=10/1+11.1%+10/(1+7.7%)^2+110/(1+7.6%)^3

$$x = \frac { 10 } { 1 + 11.1 \% } + \frac { 10 } { ( 1 + 7.7 \% ) ^ { 2 } } + \frac { 110 } { ( 1 + 7.6 \% ) ^ { 3 } }$$

Solve for x

$$x = \frac{2656959478443860000}{25084318447576971} = 105\frac{23106041448277908}{25084318447576972} \approx 105.921134911$$

Steps for Solving Linear Equation

Expand \frac{11.1}{100} by multiplying both numerator and the denominator by 10.

$$x=\frac{10}{1+\frac{111}{1000}}+\frac{10}{\left(1+\frac{7.7}{100}\right)^{2}}+\frac{110}{\left(1+\frac{7.6}{100}\right)^{3}}$$

Add 1 and \frac{111}{1000} to get \frac{1111}{1000}.

$$x=\frac{10}{\frac{1111}{1000}}+\frac{10}{\left(1+\frac{7.7}{100}\right)^{2}}+\frac{110}{\left(1+\frac{7.6}{100}\right)^{3}}$$

Divide 10 by \frac{1111}{1000} by multiplying 10 by the reciprocal of \frac{1111}{1000}.

$$x=10\times \frac{1000}{1111}+\frac{10}{\left(1+\frac{7.7}{100}\right)^{2}}+\frac{110}{\left(1+\frac{7.6}{100}\right)^{3}}$$

Multiply 10 and \frac{1000}{1111} to get \frac{10000}{1111}.

$$x=\frac{10000}{1111}+\frac{10}{\left(1+\frac{7.7}{100}\right)^{2}}+\frac{110}{\left(1+\frac{7.6}{100}\right)^{3}}$$

Expand \frac{7.7}{100} by multiplying both numerator and the denominator by 10.

$$x=\frac{10000}{1111}+\frac{10}{\left(1+\frac{77}{1000}\right)^{2}}+\frac{110}{\left(1+\frac{7.6}{100}\right)^{3}}$$

Add 1 and \frac{77}{1000} to get \frac{1077}{1000}.

$$x=\frac{10000}{1111}+\frac{10}{\left(\frac{1077}{1000}\right)^{2}}+\frac{110}{\left(1+\frac{7.6}{100}\right)^{3}}$$

Calculate \frac{1077}{1000} to the power of 2 and get \frac{1159929}{1000000}.

$$x=\frac{10000}{1111}+\frac{10}{\frac{1159929}{1000000}}+\frac{110}{\left(1+\frac{7.6}{100}\right)^{3}}$$

Divide 10 by \frac{1159929}{1000000} by multiplying 10 by the reciprocal of \frac{1159929}{1000000}.

$$x=\frac{10000}{1111}+10\times \frac{1000000}{1159929}+\frac{110}{\left(1+\frac{7.6}{100}\right)^{3}}$$

Multiply 10 and \frac{1000000}{1159929} to get \frac{10000000}{1159929}.

$$x=\frac{10000}{1111}+\frac{10000000}{1159929}+\frac{110}{\left(1+\frac{7.6}{100}\right)^{3}}$$

Add \frac{10000}{1111} and \frac{10000000}{1159929} to get \frac{22709290000}{1288681119}.

$$x=\frac{22709290000}{1288681119}+\frac{110}{\left(1+\frac{7.6}{100}\right)^{3}}$$

Expand \frac{7.6}{100} by multiplying both numerator and the denominator by 10.

$$x=\frac{22709290000}{1288681119}+\frac{110}{\left(1+\frac{76}{1000}\right)^{3}}$$

Reduce the fraction \frac{76}{1000} to lowest terms by extracting and canceling out 4.

$$x=\frac{22709290000}{1288681119}+\frac{110}{\left(1+\frac{19}{250}\right)^{3}}$$

Add 1 and \frac{19}{250} to get \frac{269}{250}.

$$x=\frac{22709290000}{1288681119}+\frac{110}{\left(\frac{269}{250}\right)^{3}}$$

Calculate \frac{269}{250} to the power of 3 and get \frac{19465109}{15625000}.

$$x=\frac{22709290000}{1288681119}+\frac{110}{\frac{19465109}{15625000}}$$

Divide 110 by \frac{19465109}{15625000} by multiplying 110 by the reciprocal of \frac{19465109}{15625000}.

$$x=\frac{22709290000}{1288681119}+110\times \frac{15625000}{19465109}$$

Multiply 110 and \frac{15625000}{19465109} to get \frac{1718750000}{19465109}.

$$x=\frac{22709290000}{1288681119}+\frac{1718750000}{19465109}$$

Add \frac{22709290000}{1288681119} and \frac{1718750000}{19465109} to get \frac{2656959478443860000}{25084318447576971}.

$$x=\frac{2656959478443860000}{25084318447576971}$$

Assign x

$$x≔\frac{2656959478443860000}{25084318447576971}$$