Solve P=[2.5+(0.15/0.10)(5-2.5)/0.10]

$$P = [ \frac { 2.5 + ( \frac { 0.15 } { 0.10 } ) ( 5 - 2.5 ) } { 0.10 } ]$$

Solve for P

$$P=62.5$$

Steps for Solving Linear Equation

Expand \frac{0.15}{0.1} by multiplying both numerator and the denominator by 100.

$$P=\frac{2.5+\frac{15}{10}\left(5-2.5\right)}{0.1}$$

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$P=\frac{2.5+\frac{3}{2}\left(5-2.5\right)}{0.1}$$

Subtract 2.5 from 5 to get 2.5.

$$P=\frac{2.5+\frac{3}{2}\times 2.5}{0.1}$$

Convert decimal number 2.5 to fraction \frac{25}{10}. Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$P=\frac{2.5+\frac{3}{2}\times \frac{5}{2}}{0.1}$$

Multiply \frac{3}{2} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$P=\frac{2.5+\frac{3\times 5}{2\times 2}}{0.1}$$

Do the multiplications in the fraction \frac{3\times 5}{2\times 2}.

$$P=\frac{2.5+\frac{15}{4}}{0.1}$$

Convert decimal number 2.5 to fraction \frac{25}{10}. Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$P=\frac{\frac{5}{2}+\frac{15}{4}}{0.1}$$

Least common multiple of 2 and 4 is 4. Convert \frac{5}{2} and \frac{15}{4} to fractions with denominator 4.

$$P=\frac{\frac{10}{4}+\frac{15}{4}}{0.1}$$

Since \frac{10}{4} and \frac{15}{4} have the same denominator, add them by adding their numerators.

$$P=\frac{\frac{10+15}{4}}{0.1}$$

Add 10 and 15 to get 25.

$$P=\frac{\frac{25}{4}}{0.1}$$

Express \frac{\frac{25}{4}}{0.1} as a single fraction.

$$P=\frac{25}{4\times 0.1}$$

Multiply 4 and 0.1 to get 0.4.

$$P=\frac{25}{0.4}$$

Expand \frac{25}{0.4} by multiplying both numerator and the denominator by 10.

$$P=\frac{250}{4}$$

Reduce the fraction \frac{250}{4} to lowest terms by extracting and canceling out 2.

$$P=\frac{125}{2}$$

Assign P

$$P≔62.5$$