Solve 4(3/5y+1/100)+5y=8/15

$$4 ( \frac { 3 } { 5 } y + \frac { 1 } { 100 } ) + 5 y = \frac { 8 } { 15 }$$

Solve for y

$$y=\frac{1}{15}\approx 0.066666667$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by \frac{3}{5}y+\frac{1}{100}.

$$4\times \frac{3}{5}y+4\times \frac{1}{100}+5y=\frac{8}{15}$$

Express 4\times \frac{3}{5} as a single fraction.

$$\frac{4\times 3}{5}y+4\times \frac{1}{100}+5y=\frac{8}{15}$$

Multiply 4 and 3 to get 12.

$$\frac{12}{5}y+4\times \frac{1}{100}+5y=\frac{8}{15}$$

Multiply 4 and \frac{1}{100} to get \frac{4}{100}.

$$\frac{12}{5}y+\frac{4}{100}+5y=\frac{8}{15}$$

Reduce the fraction \frac{4}{100} to lowest terms by extracting and canceling out 4.

$$\frac{12}{5}y+\frac{1}{25}+5y=\frac{8}{15}$$

Combine \frac{12}{5}y and 5y to get \frac{37}{5}y.

$$\frac{37}{5}y+\frac{1}{25}=\frac{8}{15}$$

Subtract \frac{1}{25} from both sides.

$$\frac{37}{5}y=\frac{8}{15}-\frac{1}{25}$$

Least common multiple of 15 and 25 is 75. Convert \frac{8}{15} and \frac{1}{25} to fractions with denominator 75.

$$\frac{37}{5}y=\frac{40}{75}-\frac{3}{75}$$

Since \frac{40}{75} and \frac{3}{75} have the same denominator, subtract them by subtracting their numerators.

$$\frac{37}{5}y=\frac{40-3}{75}$$

Subtract 3 from 40 to get 37.

$$\frac{37}{5}y=\frac{37}{75}$$

Multiply both sides by \frac{5}{37}, the reciprocal of \frac{37}{5}.

$$y=\frac{37}{75}\times \frac{5}{37}$$

Multiply \frac{37}{75} times \frac{5}{37} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{37\times 5}{75\times 37}$$

Cancel out 37 in both numerator and denominator.

$$y=\frac{5}{75}$$

Reduce the fraction \frac{5}{75} to lowest terms by extracting and canceling out 5.

$$y=\frac{1}{15}$$