At first glance, this puzzle looks incredibly easy. It gives us three equations and asks us to find the value of C:
a + a = 20
b + b = 10
a + b × c = 50
c = ?
Many people rush to the final line and start guessing. But the key to solving this puzzle is to work through the equations carefully and remember one of the most important rules in mathematics: multiplication comes before addition.
Let’s solve it step by step.
Step 1: Find the value of A
The first equation says:
a + a = 20
Since there are two identical values of a, we can write:
2a = 20
Now divide both sides by 2:
a = 10
So we know:
A = 10
Step 2: Find the value of B
The second equation is:
b + b = 10
Again, there are two identical values:
2b = 10
Divide both sides by 2:
b = 5
Therefore:
B = 5
Step 3: Use the final equation
Now we have:
a + b × c = 50
We already know that:
a = 10
and
b = 5
So substitute those values into the equation:
10 + 5 × c = 50
Now comes the important part.
According to the standard order of operations, multiplication must be performed before addition.
Therefore, we calculate:
5 × c
before adding 10.
So:
10 + 5c = 50
Subtract 10 from both sides:
5c = 40
Now divide both sides by 5:
c = 8
✅ The answer is: C = 8
Let’s Check the Answer
Whenever you solve a puzzle like this, it is a good idea to put the answer back into the original equation.
We found:
A = 10
B = 5
C = 8
Now substitute them:
10 + 5 × 8 = 50
First multiply:
5 × 8 = 40
Then add:
10 + 40 = 50
And that gives us:
50 = 50 ✅
So the solution is correct.
Why Do People Get This Puzzle Wrong?
The biggest trap is usually the last equation:
a + b × c = 50
Some people read it from left to right and calculate:
a + b = 15
Then they try to work with 15 × c.
But that’s not how the expression is evaluated.
Mathematics follows an established order of operations. Multiplication has priority over addition.
For example:
10 + 5 × 8
does not mean:
(10 + 5) × 8
Instead, it means:
10 + (5 × 8)
So:
10 + 40 = 50
This is why C = 8.
The Final Solution
The entire puzzle can be solved in just a few lines:
a + a = 20
a = 10
b + b = 10
b = 5
Then:
a + b × c = 50
10 + 5c = 50
5c = 40
c = 8
🎯 Final Answer:
8
This puzzle is a good example of why solving a math problem carefully is often more important than solving it quickly. The equations themselves are simple, but the final expression tests whether you remember the order of operations.
Did you get 8 before reading the explanation?