Question

The sum of two numbers is 16. Their difference is 6. What are the two numbers? What is their product?

Answer 1

Hint: To solve such questions, we need to assume the two unknowns as $x$ and $y$. We are given two conditions, the sum and the difference. We get two equations in two variables. Solving the two equations, we get the values of two unknowns.

Complete step by step answer:
Let’s consider the two unknown numbers as $x$ and $y$. The sum of the two numbers is 16: $x + y = 16$. The difference between the numbers is 6: $x - y = 6$. Now we have two equations with two unknowns. First we will add the two equations to find the value of $x$ and then subtract the two equations to find the value of $y$. Let’s add the two equations, we get:
$x + y + x - y = 16 + 6$
$\Rightarrow 2x = 22$
$\therefore x = 11$
Now let’s subtract the two equations, we get:
$(x + y) - (x - y) = 16 - 6$
$\Rightarrow 2y = 10$
$\therefore y = 5$

Therefore, the two numbers are 11 and 5.

Note: We can check and confirm whether our values are right or wrong by substituting them in any one of the equations. After finding the value of $x$ , we can find the value of $y$ by substituting in any one of the equations instead of subtracting them.
$11 + 5 = 16$
$\Rightarrow 11 - 5 = 6$
Hence, our two values are right.