if a-20=b and b-60=c and c+40=d and the sum of a b and c is 1725 what is the value of a

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.

Learn how to solve a system of linear equations where a - 20 = b, b - 60 = c, c + 40 = d, and the sum of a, b, and c equals 1725. This problem applies key algebraic concepts, such as solving linear equations and simplifying terms. Suitable for students in Grades 8-10.

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