Question

A number is 10 more than another number twice the sum of the two numbers is 8. Find the two numbers Please help. Thanks

Answer 1

Let x and y be the unknown numbers.

We know that one number is 10 more than the other, this can be express as:

$y=x+10$

We also know that twice the sum of both numbers is equal to 8, the sum of the two numbers is:

$x+y$

Twice this sum is:

$2(x+y)=2x+2y$

And this have to be equal to 8, then we have the equation:

$2x+2y=8$

Hence we have the system of equations:

$\begin{gathered} y=x+10 \\ 2x+2y=8 \end{gathered}$

To solve this system we take the expression for y from the first equation and plug it in the second, then we solve for x:

$\begin{gathered} 2x+2(x+10)=8 \\ 2x+2x+20=8 \\ 4x+20=8 \\ 4x=8-20 \\ 4x=-12 \\ x=-\frac{12}{4} \\ x=-3 \end{gathered}$

Now that we know the value of x we plug it in the expression for y:

$\begin{gathered} y=-3+10 \\ y=7 \end{gathered}$

Therefore the numbers we are looking for are -3 and 7