Question

In the following exercises, solve each equation with decimal coefficients.

$0.05n+0.10(n+8)=2.15$

Short answer

The value of $n$is$9$

Step-by-step solution

Step 1. Given Information 

In the given question we have to solve equation with decimal coefficients.
$0.05n+0.10(n+8)=2.15$

Step 2. The given equation is 0.05n+0.10(n+8)=2.15

Now we solve the given equation for the value of$n$

Looking at the decimals and thinking of the equivalent fractions:

$0.05=\frac{5}{100}0.10=\frac{10}{100}2.15=\frac{215}{100}$

The LCD is 100.

Step 4. By multiplying by the LCD we will clear the decimals from the equation. 

Distribute first.

$$\begin{gathered} 0.05n+0.10\times n+0.10\times 8=2.15 \\ 0.05n+0.10n+0.80=2.15 \end{gathered}$$

Combine like terms.

$0.15n+0.80=2.15$

Step 5. To clear decimals, multiply by 100.

$100\left(0.15n+0.80\right)=2.15\times 100$

Distribute.

$$\begin{gathered} 100\times 0.15n+100\times 0.80=2.15\times 100 \\ 15n+80=215 \end{gathered}$$

Step 6. Subtract 80 on both side

$$\begin{gathered} 15n+80-80=215-80 \\ 15n=135 \\ \frac{15}{15}n=\frac{135}{15} \\ n=9 \end{gathered}$$

Step 7. Now checking the value. 

putting $n=9$in the given equation

$$\begin{gathered} 0.05\times 9+0.10(9+8)=2.15 \\ 0.45+0.10\times 17=2.15 \\ 0.45+1.7=2.15 \\ 2.15=2.15 \end{gathered}$$