Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 19, 2024

Find the ratio of $x$ to $y$ given the equation $3x = 7y$ .

STEP 1

Assumptions
1. The given equation is $3x = 7y$ .
2. We need to find the ratio $x : y$ .

STEP 2

To find the ratio $x : y$ , we need to express $x$ in terms of $y$ or vice versa using the given equation.

STEP 3

We can start by isolating $x$ on one side of the equation.
$x = \frac{7y}{3}$

STEP 4

Now, we can express the ratio $x : y$ using the expression for $x$ in terms of $y$ .
$x : y = \frac{7y}{3} : y$

STEP 5

To simplify the ratio, we can divide both terms by $y$ .
$x : y = \frac{7y}{3y} : \frac{y}{y}$

STEP 6

Since any number divided by itself is equal to 1, we can simplify further.
$x : y = \frac{7}{3} : 1$

STEP 7

The ratio $x : y$ is therefore $7 : 3$ .
The ratio of $x$ to $y$ is $7 : 3$ .

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