What plus what equals 36?
Understand the Problem
The question is asking for two numbers that, when added together, equal 36. This involves identifying pairs of numbers that satisfy this equation.
Answer
The pairs of numbers that add up to 36 include $(10, 26)$, $(20, 16)$, and $(0, 36)$.
Answer for screen readers
The pairs of numbers that add up to 36 include (10, 26), (20, 16), and (0, 36).
Steps to Solve
- Identify the relationship between the numbers
We need to find two numbers, let's call them $x$ and $y$, such that their sum equals 36. This can be expressed mathematically as: $$ x + y = 36 $$
- Express one variable in terms of the other
We can express one of the numbers in terms of the other. Let's express $y$ in terms of $x$: $$ y = 36 - x $$
- Choose a value for one of the numbers
We can choose any number for $x$ and calculate $y$. Let's try a couple of values.
For example:
- If we let $x = 10$, then: $$ y = 36 - 10 = 26 $$
- Verify the pairs found
Check the sum of the pairs to confirm that they indeed add up to 36: $$ 10 + 26 = 36 $$
- Explore more pairs
We can find more pairs by choosing different values for $x$. Let's try:
- If $x = 20$, then: $$ y = 36 - 20 = 16 $$
Check the sum: $$ 20 + 16 = 36 $$
- List solutions
The pairs that satisfy $x + y = 36$ are:
- (10, 26)
- (20, 16)
- (0, 36)
The pairs of numbers that add up to 36 include (10, 26), (20, 16), and (0, 36).
More Information
This problem demonstrates the principle of finding pairs of numbers that satisfy an equation. The technique used is quite versatile and can be applied to many similar problems in algebra.
Tips
- Misunderstanding the equation and only finding one number instead of two.
- Forgetting to check that both numbers indeed add to 36.
- Assuming there is only one correct answer; there are multiple pairs of numbers.
