Harmon Bartlett
09/23/2023 · Primary School
The sum of three consecutive numbers \( a, b, c \) is 36 , find \( c-b+a \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Let the three consecutive numbers be represented as \( a \), \( b \), and \( c \). Since they are consecutive, we can express them in terms of \( a \):
\[
b = a + 1
\]
\[
c = a + 2
\]
The sum of these three numbers is given as:
\[
a + b + c = 36
\]
Substituting the expressions for \( b \) and \( c \):
\[
a + (a + 1) + (a + 2) = 36
\]
Simplifying this equation:
\[
3a + 3 = 36
\]
Subtracting 3 from both sides:
\[
3a = 33
\]
Dividing by 3:
\[
a = 11
\]
Now we can find \( b \) and \( c \):
\[
b = a + 1 = 11 + 1 = 12
\]
\[
c = a + 2 = 11 + 2 = 13
\]
Now we need to calculate \( c - b + a \):
\[
c - b + a = 13 - 12 + 11
\]
Calculating this step-by-step:
\[
c - b = 13 - 12 = 1
\]
\[
c - b + a = 1 + 11 = 12
\]
Thus, the value of \( c - b + a \) is:
\[
\boxed{12}
\]
Quick Answer
The value of \( c - b + a \) is 12.
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