Answer :
To find the two numbers, we can set up a system of equations based on the information given in the problem.
We know two things:
- The sum of the two numbers is 327.
- The difference between the two numbers is 151.
Let's define the two numbers as [tex]x[/tex] and [tex]y[/tex]. So, we can write the following equations:
[tex]\begin{align*}
x + y &= 327 \
x - y &= 151
\end{align*}[/tex]
Now, we can solve this system of equations using the elimination method.
Step 1: Add the two equations together to eliminate [tex]y[/tex].
[tex]\begin{align*}
(x + y) + (x - y) &= 327 + 151 \\
2x &= 478
\end{align*}[/tex]
Step 2: Solve for [tex]x[/tex].
[tex]x = \frac{478}{2} = 239[/tex]
Step 3: Substitute [tex]x = 239[/tex] back into one of the original equations to solve for [tex]y[/tex].
Using the first equation:
[tex]239 + y = 327[/tex]
Subtract 239 from both sides:
[tex]y = 327 - 239 = 88[/tex]
So the two numbers are 239 and 88.
