Question

The difference of two numbers is 3. Their sum is 13. Find the numbers

a
x=8 y=5

b
x=9 y = 4

c
x=10 y = 5

Answer 1

Let's denote the two numbers as \( x \) and \( y \). According to the problem, we have the following two equations:

1. \( x - y = 3 \) (the difference of the two numbers is 3)
2. \( x + y = 13 \) (the sum of the two numbers is 13)

Now, we can solve these equations step-by-step:

1. From the first equation \( x - y = 3 \), we can express \( x \) in terms of \( y \):
\[
x = y + 3
\]

2. Now, substitute \( x \) from the first equation into the second equation:
\[
(y + 3) + y = 13
\]
Simplifying this gives:
\[
2y + 3 = 13
\]
Subtracting 3 from both sides:
\[
2y = 10
\]
Dividing both sides by 2:
\[
y = 5
\]

3. Now, substitute \( y = 5 \) back into the equation for \( x \):
\[
x = 5 + 3 = 8
\]

So, the two numbers are \( x = 8 \) and \( y = 5 \).

The correct option is (a) \( x = 8, y = 5 \).