The sum of two numbers $x$ and $y$ is 153, and the value of the fraction $\frac{x}{y}$ is 0.7. What is the value of $y - x$?
To solve this problem, I will use a system of two linear equations involving $x$ and $y$. The first equation is given by the sum of the numbers: $x + y = 153$. The second equation is given by the value of the fraction: $\frac{x}{y} = 0.7$. I can rewrite the second equation as $x = 0.7y$ by multiplying both sides by $y$. Now I can substitute $x = 0.7y$ into the first equation and get $0.7y + y = 153$. Simplifying, I get $1.7y = 153$, and then dividing both sides by 1.7, I get $y = 90$. To find $x$, I can plug $y = 90$ into either equation, but I will use the second one: $x = 0.7y = 0.7 \cdot 90 = 63$. Therefore, $x = 63$ and $y = 90$. To find $y - x$, I just subtract the values of $y$ and $x$: $y - x = 90 - 63 = 27$. 