Question

The difference between two numbers is 15. If 8 is added to twice the greater number, the result is 4 less than 3 times the lesser number. Find the two numbers.

Answer 1

Answer:

Step-by-step explanation:

Let $x$ be the greater number and $y$ be the smaller number. We know that their difference is 15, so we have

$x-y=15$

Then, we have the following information: if we add twice the greater (2x) and 8 (2x+8), the result is 3 times the lesser (3y) minus four (3y-4). So, we have

$2x+8 = 3y-4 \iff 2x-3y = -12$

So, we have the follwing system:

$\begin{cases} x-y=15\\2x-3y = -12\end{cases}$

From the first equation, we can derive $x = y+15$, and substitute this expression in the second equation to get

$2(y+15)-3y = -12 \iff 2y + 30 -3y = -12 \iff -y = -42 \iff y = 42$

Substitute this value for y in the first equation to get

$x-42=15 \iff x=15+42 \iff x = 57$