Question

The difference of one-third a number and two times another number is -5. The first number is five more than twice the second number. Enter the larger of the two numbers.

Answer 1

Let's use the variable x to represent the first number and y to represent the other number.

So, the expression "The difference of one-third a number and two times another number is -5" can be translated into the equation:

$\frac{1}{3}x-2y=-5$

Then, the other expression "The first number is five more than twice the second number" cab be translated into the equation:

$x=2y+5$

Using this value of x from the second equation into the first one, we have:

$\begin{gathered} \frac{1}{3}(2y+5)-2y=-5 \\ 2y+5-6y=-15 \\ -4y=-20 \\ y=5 \\ \\ x=2\cdot5+5=15 \end{gathered}$

Therefore the larger of the two numbers is 15.