Assume the numbers using the given ratio

Since the ratio of the two numbers is given as 5:7, let the numbers be represented as $5x$ and $7x$, where $x$ is a common positive multiplier.

$\text{Numbers} = 5x \text{ and } 7x$

Set up the equation using the given sum

We are given that the sum of these two numbers is 144. Therefore, set up the linear equation: $5x + 7x = 144$.

$5x + 7x = 144$

Solve for the multiplier x

Combine like terms to get $12x = 144$, and divide both sides by 12 to find the value of $x$.

$x = \frac{144}{12} = 12$

Calculate the larger number

The larger number corresponds to the ratio part $7x$. Substitute $x = 12$ into $7x$ to find the final value.

$7 \times 12 = 84$