We are given the following system of equations:

1. $a - 20 = b$
2. $b - 60 = c$
3. $c + 40 = d$
4. $a + b + c = 1725$

We need to find the value of $a$.

Step 1: Express $b$ and $c$ in terms of $a$

From the first equation: $b = a - 20$

From the second equation: $c = b - 60 = (a - 20) - 60 = a - 80$

Step 2: Substitute $b$ and $c$ in the sum equation

We are given that $a + b + c = 1725$. Substituting $b = a - 20$ and $c = a - 80$ into this equation:

$a + (a - 20) + (a - 80) = 1725$

Step 3: Simplify the equation

Simplifying the left-hand side:

$a + a - 20 + a - 80 = 1725$ $3a - 100 = 1725$

Step 4: Solve for $a$

Add 100 to both sides: $3a = 1825$

Now, divide by 3: $a = \frac{1825}{3} = 608.33$

So, the value of $a$ is approximately $608.33$.

Would you like further clarification or a breakdown of any specific step?

Here are 5 related questions:

1. How would you solve if the sum was different?
2. Can you verify the values of $b$, $c$, and $d$ with the found $a$?
3. How would this change if another equation was introduced?
4. What happens if all values must be integers?
5. Can this system of equations be solved using matrices?

Tip: Always double-check by substituting values back into the original equations to ensure correctness.