Solve 25/125=360/7-160/250y/180-7

$$\frac { 25 } { 125 } = \frac { \frac { 360 } { 7 } - \frac { 160 } { 250 } y } { 180 - 7 }$$

Solve for y

$$y = \frac{2945}{112} = 26\frac{33}{112} \approx 26.294642857$$

Steps for Solving Linear Equation

Reduce the fraction \frac{25}{125} to lowest terms by extracting and canceling out 25.

$$\frac{1}{5}=\frac{\frac{360}{7}-\frac{160}{250}y}{180-7}$$

Reduce the fraction \frac{160}{250} to lowest terms by extracting and canceling out 10.

$$\frac{1}{5}=\frac{\frac{360}{7}-\frac{16}{25}y}{180-7}$$

Subtract 7 from 180 to get 173.

$$\frac{1}{5}=\frac{\frac{360}{7}-\frac{16}{25}y}{173}$$

Divide each term of \frac{360}{7}-\frac{16}{25}y by 173 to get \frac{360}{1211}-\frac{16}{4325}y.

$$\frac{1}{5}=\frac{360}{1211}-\frac{16}{4325}y$$

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

$$\frac{360}{1211}-\frac{16}{4325}y=\frac{1}{5}$$

Subtract \frac{360}{1211} from both sides.

$$-\frac{16}{4325}y=\frac{1}{5}-\frac{360}{1211}$$

Least common multiple of 5 and 1211 is 6055. Convert \frac{1}{5} and \frac{360}{1211} to fractions with denominator 6055.

$$-\frac{16}{4325}y=\frac{1211}{6055}-\frac{1800}{6055}$$

Since \frac{1211}{6055} and \frac{1800}{6055} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{16}{4325}y=\frac{1211-1800}{6055}$$

Subtract 1800 from 1211 to get -589.

$$-\frac{16}{4325}y=-\frac{589}{6055}$$

Multiply both sides by -\frac{4325}{16}, the reciprocal of -\frac{16}{4325}.

$$y=-\frac{589}{6055}\left(-\frac{4325}{16}\right)$$

Multiply -\frac{589}{6055} times -\frac{4325}{16} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{-589\left(-4325\right)}{6055\times 16}$$

Do the multiplications in the fraction \frac{-589\left(-4325\right)}{6055\times 16}.

$$y=\frac{2547425}{96880}$$

Reduce the fraction \frac{2547425}{96880} to lowest terms by extracting and canceling out 865.

$$y=\frac{2945}{112}$$