There are two numbers. The sum of the first number and double the second is 42. Four times the difference between the second and the first number gives us the first number. What is the product of the two numbers?
Solution
If $a$ and $b$ are the two numbers,
then $a+2b=42$ and also $4(b-a)= a$ or $4b=5a$
Since $a+2b=42$
$\Rightarrow 2a+4b=84$
$\Rightarrow 2a+5a=84$
$\Rightarrow 7a=84$
$\Rightarrow a=12$
And $b=15$
Thus, $a \times b=180$