# If 3(x + 12) = 4(y + 9), what is the ratio of x to y?

## Question:

If 3(x + 12) = 4(y + 9), what is the ratio of x to y?

## Ratios: Evaluating a Quotient

A ratio of two numbers {eq}a {/eq} and {eq}b {/eq}, also known as quotient, can be evaluated by a fraction in which our first number, {eq}a {/eq}, belongs to the numerator and our second number, {eq}b {/eq}, belongs to the denominator. If a fraction can be simplified, we can express the ratio as either a simplified fraction {eq}\frac{a}{b} {/eq} or a number that we obtain dividing {eq}a {/eq} by {eq}b {/eq}.

Let's solve the given equation using the distributive property:

{eq}3(x + 12) = 3x + 36\\ 4(y + 9) = 4y + 36 {/eq}

We know that:

{eq}3x + 36 = 4y + 36 {/eq}

Subtract 36 from both sides:

{eq}3x = 4y {/eq}

We can now divide both sides by 3y:

{eq}\frac{3x}{3y} = \frac{4y}{3y}\\ \frac{x}{y} = \frac{4}{3} {/eq}

Therefore, the ratio of x to y is {eq}\boxed{\frac{4}{3}} {/eq}