What is the missing number?
$73 - 17 = 46 + ?$
The problem asks us to find the missing number in the equation \(73 - 17 = 46 + ?\). Let the missing number be denoted by \(x\). The equation is thus:
\[73 - 17 = 46 + x\]
To solve for \(x\), we first evaluate the subtraction on the left-hand side. Calculating \(73 - 17\):
\[73 - 10 = 63\]
\[63 - 7 = 56\]
So, the equation simplifies to:
\[56 = 46 + x\]
Now that we have the equation \(56 = 46 + x\), we isolate \(x\) by subtracting 46 from both sides of the equation:
\[x = 56 - 46\]
Performing the subtraction:
\[56 - 46 = 10\]
Therefore, the value of the missing number \(x\) is \(10\). Comparing this result with the given options (a: 8, b: 10, c: 12, d: 13), we see that the correct choice is b.
In daily life, solving for an unknown in an equation is like balancing a scale. For example, if you have a collection of 73 marbles and lose 17, you are left with 56 marbles. If you know you already put 46 marbles in a box, you can calculate exactly how many more marbles \(x\) you need to add to match the 56 marbles remaining: \(56 - 46 = 10\). This simple algebraic reasoning is essential for managing budgets, inventory, or any situation requiring quantitative balance.