Solve (1/40+1/40+1/40+1/2)varphi=20+20+20

$$( \frac { 1 } { 40 } + \frac { 1 } { 40 } + \frac { 1 } { 40 } + \frac { 1 } { 2 } ) \varphi = 20 + 20 + 20$$

Solve for φ

$$\phi =\frac{2400}{23}\approx 104.347826087$$

Steps for Solving Linear Equation

Since \frac{1}{40} and \frac{1}{40} have the same denominator, add them by adding their numerators.

$$\left(\frac{1+1}{40}+\frac{1}{40}+\frac{1}{2}\right)\phi =20+20+20$$

Add 1 and 1 to get 2.

$$\left(\frac{2}{40}+\frac{1}{40}+\frac{1}{2}\right)\phi =20+20+20$$

Reduce the fraction \frac{2}{40} to lowest terms by extracting and canceling out 2.

$$\left(\frac{1}{20}+\frac{1}{40}+\frac{1}{2}\right)\phi =20+20+20$$

Least common multiple of 20 and 40 is 40. Convert \frac{1}{20} and \frac{1}{40} to fractions with denominator 40.

$$\left(\frac{2}{40}+\frac{1}{40}+\frac{1}{2}\right)\phi =20+20+20$$

Since \frac{2}{40} and \frac{1}{40} have the same denominator, add them by adding their numerators.

$$\left(\frac{2+1}{40}+\frac{1}{2}\right)\phi =20+20+20$$

Add 2 and 1 to get 3.

$$\left(\frac{3}{40}+\frac{1}{2}\right)\phi =20+20+20$$

Least common multiple of 40 and 2 is 40. Convert \frac{3}{40} and \frac{1}{2} to fractions with denominator 40.

$$\left(\frac{3}{40}+\frac{20}{40}\right)\phi =20+20+20$$

Since \frac{3}{40} and \frac{20}{40} have the same denominator, add them by adding their numerators.

$$\frac{3+20}{40}\phi =20+20+20$$

Add 3 and 20 to get 23.

$$\frac{23}{40}\phi =20+20+20$$

Add 20 and 20 to get 40.

$$\frac{23}{40}\phi =40+20$$

Add 40 and 20 to get 60.

$$\frac{23}{40}\phi =60$$

Multiply both sides by \frac{40}{23}, the reciprocal of \frac{23}{40}.

$$\phi =60\times \frac{40}{23}$$

Express 60\times \frac{40}{23} as a single fraction.

$$\phi =\frac{60\times 40}{23}$$

Multiply 60 and 40 to get 2400.

$$\phi =\frac{2400}{23}$$