Solve for p 3/5(1+p)=21/20

$\frac{3}{5} (1 + p) = \frac{21}{20}$

Step 1

Multiply both sides of the equation by $\frac{5}{3}$ .

$\frac{5}{3} (\frac{3}{5} \cdot (1 + p)) = \frac{5}{3} \cdot \frac{21}{20}$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{5}{3} (\frac{3}{5} \cdot (1 + p))$ .

Apply the distributive property.

$\frac{5}{3} (\frac{3}{5} \cdot 1 + \frac{3}{5} p) = \frac{5}{3} \cdot \frac{21}{20}$

Multiply $\frac{3}{5}$ by $1$ .

$\frac{5}{3} (\frac{3}{5} + \frac{3}{5} p) = \frac{5}{3} \cdot \frac{21}{20}$

Combine $\frac{3}{5}$ and $p$ .

$\frac{5}{3} (\frac{3}{5} + \frac{3 p}{5}) = \frac{5}{3} \cdot \frac{21}{20}$

Apply the distributive property.

$\frac{5}{3} \cdot \frac{3}{5} + \frac{5}{3} \cdot \frac{3 p}{5} = \frac{5}{3} \cdot \frac{21}{20}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5}{3} \cdot \frac{3}{5} + \frac{5}{3} \cdot \frac{3 p}{5} = \frac{5}{3} \cdot \frac{21}{20}$

Rewrite the expression.

$\frac{1}{3} \cdot 3 + \frac{5}{3} \cdot \frac{3 p}{5} = \frac{5}{3} \cdot \frac{21}{20}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{1}{3} \cdot 3 + \frac{5}{3} \cdot \frac{3 p}{5} = \frac{5}{3} \cdot \frac{21}{20}$

Rewrite the expression.

$1 + \frac{5}{3} \cdot \frac{3 p}{5} = \frac{5}{3} \cdot \frac{21}{20}$

Cancel the common factor of $5$ .

Cancel the common factor.

$1 + \frac{5}{3} \cdot \frac{3 p}{5} = \frac{5}{3} \cdot \frac{21}{20}$

Rewrite the expression.

$1 + \frac{1}{3} (3 p) = \frac{5}{3} \cdot \frac{21}{20}$

Cancel the common factor of $3$ .

Factor $3$ out of $3 p$ .

$1 + \frac{1}{3} (3 (p)) = \frac{5}{3} \cdot \frac{21}{20}$

Cancel the common factor.

$1 + \frac{1}{3} (3 p) = \frac{5}{3} \cdot \frac{21}{20}$

Rewrite the expression.

$1 + p = \frac{5}{3} \cdot \frac{21}{20}$

Simplify the right side.

Simplify $\frac{5}{3} \cdot \frac{21}{20}$ .

Cancel the common factor of $5$ .

Factor $5$ out of $20$ .

$1 + p = \frac{5}{3} \cdot \frac{21}{5 (4)}$

Cancel the common factor.

$1 + p = \frac{5}{3} \cdot \frac{21}{5 \cdot 4}$

Rewrite the expression.

$1 + p = \frac{1}{3} \cdot \frac{21}{4}$

Cancel the common factor of $3$ .

Factor $3$ out of $21$ .

$1 + p = \frac{1}{3} \cdot \frac{3 (7)}{4}$

Cancel the common factor.

$1 + p = \frac{1}{3} \cdot \frac{3 \cdot 7}{4}$

Rewrite the expression.

$1 + p = \frac{7}{4}$

Step 3

Move all terms not containing $p$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$p = \frac{7}{4} - 1$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$p = \frac{7}{4} - 1 \cdot \frac{4}{4}$

Combine $- 1$ and $\frac{4}{4}$ .

$p = \frac{7}{4} + \frac{- 1 \cdot 4}{4}$

Combine the numerators over the common denominator.

$p = \frac{7 - 1 \cdot 4}{4}$

Simplify the numerator.

Multiply $- 1$ by $4$ .

$p = \frac{7 - 4}{4}$

Subtract $4$ from $7$ .

$p = \frac{3}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$p = \frac{3}{4}$

Decimal Form:

$p = 0.75$

Solve for p 3/5(1+p)=21/20

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