Solve {l}{2/28=p/35}{0.9/1.5=a/10}{frac{3.6}{9}=frac{b}{0.5}}

$$\left. \begin{array} { l } { \frac { 2 } { 28 } = \frac { p } { 35 } } \\ { \frac { 0.9 } { 1.5 } = \frac { a } { 10 } } \\ { \frac { 3.6 } { 9 } = \frac { b } { 0.5 } } \end{array} \right.$$

Solve for p, a, b

$$p=2.5$$

$$a=6$$

$$b=0.2$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 140, the least common multiple of 28,35.

$$5\times 2=4p$$

Multiply 5 and 2 to get 10.

$$10=4p$$

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

$$4p=10$$

Divide both sides by 4.

$$p=\frac{10}{4}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$p=\frac{5}{2}$$

Consider the second equation. Multiply both sides of the equation by 10.

$$10\times \frac{0.9}{1.5}=a$$

Expand \frac{0.9}{1.5} by multiplying both numerator and the denominator by 10.

$$10\times \frac{9}{15}=a$$

Reduce the fraction \frac{9}{15} to lowest terms by extracting and canceling out 3.

$$10\times \frac{3}{5}=a$$

Multiply 10 and \frac{3}{5} to get 6.

$$6=a$$

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

$$a=6$$

Consider the third equation. Expand \frac{3.6}{9} by multiplying both numerator and the denominator by 10.

$$\frac{36}{90}=\frac{b}{0.5}$$

Reduce the fraction \frac{36}{90} to lowest terms by extracting and canceling out 18.

$$\frac{2}{5}=\frac{b}{0.5}$$

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

$$\frac{b}{0.5}=\frac{2}{5}$$

Multiply both sides by 0.5.

$$b=\frac{2}{5}\times 0.5$$

Multiply \frac{2}{5} and 0.5 to get \frac{1}{5}.

$$b=\frac{1}{5}$$

The system is now solved.

$$p=\frac{5}{2} a=6 b=\frac{1}{5}$$