Solve by Substitution m+n=1000 0.05m+0.06n=57

$m + n = 1000$ $0.05 m + 0.06 n = 57$

Step 1

Subtract $n$ from both sides of the equation.

$m = 1000 - n$

$0.05 m + 0.06 n = 57$

Step 2

Replace all occurrences of $m$ with $1000 - n$ in each equation.

Replace all occurrences of $m$ in $0.05 m + 0.06 n = 57$ with $1000 - n$ .

$0.05 (1000 - n) + 0.06 n = 57$

$m = 1000 - n$

Simplify the left side.

Simplify $0.05 (1000 - n) + 0.06 n$ .

Simplify each term.

Apply the distributive property.

$0.05 \cdot 1000 + 0.05 (- n) + 0.06 n = 57$

$m = 1000 - n$

Multiply $0.05$ by $1000$ .

$50 + 0.05 (- n) + 0.06 n = 57$

$m = 1000 - n$

Multiply $- 1$ by $0.05$ .

$50 - 0.05 n + 0.06 n = 57$

$m = 1000 - n$

$50 - 0.05 n + 0.06 n = 57$

$m = 1000 - n$

Add $- 0.05 n$ and $0.06 n$ .

$50 + 0.01 n = 57$

$m = 1000 - n$

$50 + 0.01 n = 57$

$m = 1000 - n$

$50 + 0.01 n = 57$

$m = 1000 - n$

$50 + 0.01 n = 57$

$m = 1000 - n$

Step 3

Solve for $n$ in $50 + 0.01 n = 57$ .

Move all terms not containing $n$ to the right side of the equation.

Subtract $50$ from both sides of the equation.

$0.01 n = 57 - 50$

$m = 1000 - n$

Subtract $50$ from $57$ .

$0.01 n = 7$

$m = 1000 - n$

$0.01 n = 7$

$m = 1000 - n$

Divide each term in $0.01 n = 7$ by $0.01$ and simplify.

Divide each term in $0.01 n = 7$ by $0.01$ .

$\frac{0.01 n}{0.01} = \frac{7}{0.01}$

$m = 1000 - n$

Simplify the left side.

Cancel the common factor of $0.01$ .

Cancel the common factor.

$\frac{0.01 n}{0.01} = \frac{7}{0.01}$

$m = 1000 - n$

Divide $n$ by $1$ .

$n = \frac{7}{0.01}$

$m = 1000 - n$

$n = \frac{7}{0.01}$

$m = 1000 - n$

$n = \frac{7}{0.01}$

$m = 1000 - n$

Simplify the right side.

Divide $7$ by $0.01$ .

$n = 700$

$m = 1000 - n$

$n = 700$

$m = 1000 - n$

$n = 700$

$m = 1000 - n$

$n = 700$

$m = 1000 - n$

Step 4

Replace all occurrences of $n$ with $700$ in each equation.

Replace all occurrences of $n$ in $m = 1000 - n$ with $700$ .

$m = 1000 - (700)$

$n = 700$

Simplify the right side.

Simplify $1000 - (700)$ .

Multiply $- 1$ by $700$ .

$m = 1000 - 700$

$n = 700$

Subtract $700$ from $1000$ .

$m = 300$

$n = 700$

$m = 300$

$n = 700$

$m = 300$

$n = 700$

$m = 300$

$n = 700$

Step 5

List all of the solutions.

$m = 300, n = 700$

Solve by Substitution m+n=1000 0.05m+0.06n=57

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