To solve the equation, we have to isolate the variable on one side. Note that the coefficient of

p

is a rational number. Therefore, we will multiply both sides of the equation by its multiplicative inverse.

60 = \frac{3}{4} p

$LHS \cdot \frac{4}{3} = RHS \cdot \frac{4}{3}$

\frac{4}{3} \cdot 60 = \frac{4}{3} \cdot \frac{3}{4} p

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

\frac{4 \cdot 6 0}{3} = \frac{4}{3} \cdot \frac{3}{4} p

Split into factors

\frac{4 \cdot 3 \cdot 2 0}{3} = \frac{4}{3} \cdot \frac{3}{4} p

Cancel out common factors

\frac{4 \cdot 3 \cdot 2 0}{3} = \frac{4}{3} \cdot \frac{3}{4} p

Simplify quotient

4 \cdot 20 = p

80 = p

Rearrange equation

p = 80

To check that this solution is correct, let's substitute

p = 80

into the original equation and simplify.

60 = \frac{3}{4} p

$p = 80$

60 = ? \frac{3}{4} \cdot 80

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

60 = ? \frac{3 \cdot 8 0}{4}

60 = ? \frac{2 4 0}{4}

Calculate quotient

60 = 60 ✓

Since the left-hand side and right-hand side are equal,

p = 80

is the correct solution.

Exercise