Solve by Substitution a+b+c=180 , b=3a , c=5a

$a + b + c = 180$ , $b = 3 a$ , $c = 5 a$

Step 1

Replace all occurrences of $b$ with $3 a$ in each equation.

Replace all occurrences of $b$ in $a + b + c = 180$ with $3 a$ .

$a + 3 a + c = 180$

$b = 3 a$

$c = 5 a$

Simplify the left side.

Simplify $a + 3 a + c$ .

Remove parentheses.

$a + 3 a + c = 180$

$b = 3 a$

$c = 5 a$

Add $a$ and $3 a$ .

$4 a + c = 180$

$b = 3 a$

$c = 5 a$

$4 a + c = 180$

$b = 3 a$

$c = 5 a$

$4 a + c = 180$

$b = 3 a$

$c = 5 a$

$4 a + c = 180$

$b = 3 a$

$c = 5 a$

Step 2

Replace all occurrences of $c$ with $5 a$ in each equation.

Replace all occurrences of $c$ in $4 a + c = 180$ with $5 a$ .

$4 a + 5 a = 180$

$b = 3 a$

$c = 5 a$

Simplify the left side.

Simplify $4 a + 5 a$ .

Remove parentheses.

$4 a + 5 a = 180$

$b = 3 a$

$c = 5 a$

Add $4 a$ and $5 a$ .

$9 a = 180$

$b = 3 a$

$c = 5 a$

$9 a = 180$

$b = 3 a$

$c = 5 a$

$9 a = 180$

$b = 3 a$

$c = 5 a$

$9 a = 180$

$b = 3 a$

$c = 5 a$

Step 3

Divide each term in $9 a = 180$ by $9$ and simplify.

Divide each term in $9 a = 180$ by $9$ .

$\frac{9 a}{9} = \frac{180}{9}$

$b = 3 a$

$c = 5 a$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 a}{9} = \frac{180}{9}$

$b = 3 a$

$c = 5 a$

Divide $a$ by $1$ .

$a = \frac{180}{9}$

$b = 3 a$

$c = 5 a$

$a = \frac{180}{9}$

$b = 3 a$

$c = 5 a$

$a = \frac{180}{9}$

$b = 3 a$

$c = 5 a$

Simplify the right side.

Divide $180$ by $9$ .

$a = 20$

$b = 3 a$

$c = 5 a$

$a = 20$

$b = 3 a$

$c = 5 a$

$a = 20$

$b = 3 a$

$c = 5 a$

Step 4

Replace all occurrences of $a$ with $20$ in each equation.

Replace all occurrences of $a$ in $b = 3 a$ with $20$ .

$b = 3 (20)$

$a = 20$

$c = 5 a$

Simplify the right side.

Multiply $3$ by $20$ .

$b = 60$

$a = 20$

$c = 5 a$

$b = 60$

$a = 20$

$c = 5 a$

Replace all occurrences of $a$ in $c = 5 a$ with $20$ .

$c = 5 (20)$

$b = 60$

$a = 20$

Simplify the right side.

Multiply $5$ by $20$ .

$c = 100$

$b = 60$

$a = 20$

$c = 100$

$b = 60$

$a = 20$

$c = 100$

$b = 60$

$a = 20$

Step 5

List all of the solutions.

$c = 100, b = 60, a = 20$

Solve by Substitution a+b+c=180 , b=3a , c=5a

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