Question

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

$0.05n+0.10(n+7)=3.55$

Short answer

The value of $n$is$19$

Step-by-step solution

Step 1. Given Information 

In the given question we have to solve equation with decimal coefficients.
$0.05n+0.10(n+7)=3.55$

Step 2. The given equation is 0.05n+0.10(n+7)=3.55

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

Looking at the decimals and thinking of the equivalent fractions:

$0.05=\frac{5}{100}0.10=\frac{10}{100}3.55=\frac{355}{100}$

The LCD is 100.

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

Distribute first.

$$\begin{gathered} 0.05n+0.10\times n+0.10\times 7=3.55 \\ 0.05n+0.10n+0.70=3.55 \end{gathered}$$

Combine like terms.

$0.15n+0.70=3.55$

Step 5. To clear decimals, multiply by 100.

$100(0.15n+0.70)=100\times 3.55$

Distribute.

$$\begin{gathered} 100\times 0.15n+100\times 0.70=100\times 3.55 \\ 15n+70=355 \end{gathered}$$

Step 6. Subtract 70 on both side

$$\begin{gathered} 15n+70-70=355-70 \\ 15n=285 \\ \frac{15}{15}n=\frac{285}{15} \\ n=19 \end{gathered}$$

Step 7. Now checking the value. 

putting $n=19$in the given equation

$$\begin{gathered} 0.05\times 19+0.10(19+7)=3.55 \\ 0.95+0.10\times 26=3.55 \\ 0.95+2.6=3.55 \\ 3.55=3.55 \end{gathered}$$