Question

Sum of two numbers is 53 and their difference is 11. Find out the numbers.

Answer 1

Explanation:

This is a "system of equations" problem. We have two unknowns, let's call them x & y, and we know two relationships between them, which are:

• x + y = 53
• x - y = 11

To solve this system of equations:

• Solve one of the equations for one of the variables.
• Substitute that expression into the other equation.
• Find what the other variable equals. It'll be a number.
• Put that number into either equation to find the other variable.

It doesn't matter which equation or variable you choose.

But the second one is a little simpler to solve for x:

• x - y = 11
• x = y + 11

So now we have an expression that represents x as a relationship with y. We need to substitute that into the other equation:

• x + y = 53 substitute:
• (y + 11) + y = 53 (notice we only have y terms now)
• y + 11 + y = 53
• 2y + 11 = 53
• 2y = 42
• y = 21

That's one of the numbers. We find the other number by substituting 21 into either equation as y:

• x - y = 11 substitute:
• x - 21 = 11
• x = 32

Check our work:

• Do 21 and 32 sum to 53? Yes.
• Is their difference 11? Yes.

So our answers must be correct.